I am reading Lee's *Introduction to Smooth Manifolds* and got stuck on the problem 5.6. The question is written [here, question 1.](http://www.math.ku.dk/~stancu/RiemannianGeometry/MandatoryHmwk1.pdf) (There is a typo in the question. The last sentence should be "Show that F is smoothly isomorphic...")

I do not know how to use the transition function in order to show that these bundles are isomorphic. I tried to find smooth trivializations of F, but I could not.

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Edit: [This is](http://books.google.com/books?id=eqfgZtjQceYC&pg=PA105) how Lee defined the Möbius bundle in his book. (Lee, page 105, example 5.2)