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I am reading Lee's Introduction to Smooth Manifolds and got stuck on the problem 5.6. The question is written here, question 1. (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.


Edit: This is how Lee defined the Möbius bundle in his book. (Lee, page 105, example 5.2)

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    It is more or less impossible to answer without know how the Moebius bundle was defined!2011-12-04

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