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