I wanted to know how can I prove there are only two twisted I bundle over the Klein bottle. As I looked some topology texts, I couldn't find any solid definition of twisted I-bundle (or general definition of twisted fiber bundle) except that it is not the trivial product bundle $K\times I$(K is the Klein bottle). I was looking to finding out
(1)How can I show that $K\tilde{\times}I$ is orientable?
(2)why there are only two $K\tilde{\times}I$?
I would appreciate any help anyone can give me. Also, any references to this subject might do the job.
Edith: I have denoted the twisted I bundle over the Klein bottle by $K\tilde{\times}I$