Is mere possession of a still illegal, or does need to actually be making alcohol with it?
I would hope not, everyone would be guilty of owning a still under 'constructive possision' by the ordinary everyday objects that are lying around the home.
I wouldn't distill water anyhow. Its very energy intensive, and a lot impurities are not easy to remove by distillation- especially from water.
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There are all sorts of nasty things that can get into ground water that a filter won't remove for you.
I make bottled water my primary source. I figure it's safer to rely on water that was safe to begin with, than to take water known to be unsafe and try to bring it back into spec.
Therein lies the rub. If you need to be mobile, bottled water is very heavy, but a water purified is portable. If you are stayin in one place, your water stock will run out faster than you think. You need another way to get water pure enough to drink. It doesn't need to meet EPA or Clean Air Act standards, but good enough that contagions are removed to keep you from getting immediately sick.
If its a short term emergency, drinking water with some contaminants for a few days or a few weeks isn't going to matter much. If its a TEOTWAWKI situation, your lifespan is going to be cut in half anyhow, so the main thing you need to worry about is disease.