I have heard quite a few times that they talk about say, "the" twisted S^2-bundle over S^2. My question is what do they mean by a twisted bundle? I know that in the above example any S^2-bundle over S^2 is either S^2 x S^2 or or a unique non-trivial S^2-bundle over S^2. but is that how it is defined? I mean is a twisted bundle just a non-trivial one? or is it a specific bundle among the non-trivial ones?