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What I don't understand about these bunker system; is that they can guarantee food, they can guarantee water, if it is stored in large quantities, but the air, as they purify contaminated air to survive.

They can't really guarantee anything, all they can do is prepare for what they think might happen, and hope that they were right.

Yes, yes, everyone will do what they can; The only thing I am sure of is that in a nuclear war no one wins, but one side will surely have new systems to influence the final result, whether attack or defense; and of course spies from both sides will play a key role.