Those are three different words for a reason; the differences between them are subtle, but important.
'Freedom' , according to Merriam-Webster's Reliable Book, is the state of being 'free': not restrained, not taxed, not priced, not attached or bound, and having liberty or independence. It implies both action ("winning free", "breaking free", etc.) and some nearby hostility or threat of enslavement against which one must be watchful and fiercely defensive.
'Liberty' is also the state or quality of being free, with a hint of going beyond normal limits, but its implications are more tranquil or confident. It carries no associated sense of threat, but assumes that being free to do as you like is one's natural state, and that any attempt to restrain one's liberty is a bizarre oddity.
'Independence' – again, the state of being free – has wider implications: of not being governed or bound by another, but also "not requiring or relying on something or somebody else", and "not easily influenced" – in other words, self-reliant.
It's historically notable that the rebels of the American Revolution used the words 'independence' and 'liberty' more than 'freedom'. This reveals that the colonials assumed they had already been living in 'liberty' when the British government began trying to take it away. They were already used to personal 'independence'; the vast majority of Americans then were at least subsistence farmers, or had small businesses usually connected with farming, which meant that the one tactic Britain could never use against them was to try to starve them into submission. The common self-reliance of the average citizen is what gave them the capability of winning the war, as well as the attitude that made them rebel in the first place. Americans were used to providing necessities for themselves, and even a few luxuries (such as silverware), and when Britain began leeching away too much of their hard-made wealth they could reasonably ask themselves what America really needed Britain for.
Independence, being the exact opposite of interdependence, is clearly a threat to the "Peace of Dives", which relies for its success on everybody being indebted to, and reliant on, everybody else. The idea of personal independence – self-reliance and freedom, right down to the level of the individual – is anathema to the Globalist political campaign, and to political and financial organizations supporting it. This accounts for such apparently unconnected phenomena as NAFTA, gun-control laws, financial institutions refusing to make small loans (or making them at outrageous interest), the EPA banning children's lemonade stands, various governments trying to control the Internet, and Monsanto suing small farmers into bankruptcy for even accidental possession of "patented" food-plants. Yes, Globalism is the attempt to create a single planetary government, with a single world-wide economy made up of an aristocracy of giant industries, with no individual variation allowed – all in the name of world peace.
It can't be done, of course, and even the attempt is already creating a self-reliance backlash.
Back in the 1960s and '70s, it was politically left-wing Hippies who struck out into the 'wilderness' (or at least the countryside) to create independent farming and manufacturing communes. As with any new mutation or new industry, 90% of them failed – but the few that survived managed to survive well, and have quietly created templates for successors. It's intriguing that the effort caused the pacifistic Hippies to take up and seriously study the use of firearms.
In the 1980s and '90s, it was politically right-wing Survivalists who struck out into the 'wilderness' (etc.) to create independent 'retreats' (which they would never ever call 'communes'). Besides the same market/evolutionary forces pushing 90% of them into failure, they also faced a concerted legal and propaganda campaign against them – culminating in the attack on the Branch Davidian "compound" in Waco. The government in particular considered the almost-religiously armed and business-savvy Survivalists more of a threat than the pacifistic and naive Hippies. Nonetheless, a few survived – sadder and wiser. Ironically, they learned of necessity to take a serious interest in organic farming and environmental concerns.
Nowadays, in the face of a continuing Depression and the growth of the economic aristocracy – the "1%" – the pro-independence crowd comes from all across the political spectrum. The left-wingers don't give themselves any particular label, which makes it hard for the media to smear them, and connect only by personal contact or social internet links, which makes it hard for the government to identify them. The right-wingers tend to call themselves "preppers" – as in "preparing" for disastrous social collapse – and even there the media has difficulty propagandizing against them because the original "prepper" organization, which charges its members to keep personal caches of a year's food, is the large and powerful Mormon church.
What they all have in common is a growing trend toward independence and self-reliance: providing their own defense, food, medicine, communications and – thanks to the explosive growth of 3D printing – manufacturing. All over the internet (and other nets) one can find information on how to provide these things from the individual level on up. With aquaponics one can grow food in a studio apartment. With a small solar-electric or wind-generator system a house can provide its own power. With a print-on-demand set-up a small publisher can successfully reach buyers anywhere in the world. With a basic fuel-ethanol kit a small farm can create its own fuel. And with a small 3-D printer (getting cheaper all the time) a tiny business can make anything from guns to car-parts.
All of these systems are spreading by leaps and bounds. The last time I went to a house-party to sing, all I had to do was mention the words "organic garden" and every guest had a success story to tell and technical advice to give. The self-reliance movement, for lack of a better label, is spreading faster than any government – even with the NSA spying frantically – can keep track of, let alone curtail.
There is a long-established tradition of independence in American culture, not to mention 'liberty' and 'freedom', too deeply entrenched for the best efforts of the government, the aristocracy and their obedient media to root out. This, even more than the collapsing Peace of Dives, spells defeat for the Globalist movement and its hopeful riders. As the global economy slides toward worldwide collapse, we'll soon see the financial aristocracy holding all the money but none of the real production – which will be irretrievably scattered among the independent population. In the words of Kipling, once again:
"So, though we had plenty of money,
There was nothing our money could buy.
And the gods of the copy-book headings
Said: 'If you don't work, you will die'."