möbius doble cover

The set E=M\ddot{o}\stackrel{\sim}\times I is an orientable 3-manifold with boundary. In the illustration we see in orange the möbius band at \frac{1}{2} and a small regular neigbourhood of her removed without her, i.e., if Q={\cal{N}}(M\ddot{o}\times \frac{1}{2})\smallsetminus (M\ddot{o}\times \frac{1}{2})\subset E, then which is E\smallsetminus Q?














the last step is M\ddot{o}\times\frac{1}{2} in orange, and M\ddot{o}\stackrel{\sim}\times I without M\ddot{o}\stackrel{\sim}\times (\frac{1}{2}-\varepsilon, \frac{1}{2}+\varepsilon), for \varepsilon=|\varepsilon|\to \frac{1}{2}


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