I am reading the first chapter from Topology by Armstrong. There, after stating the classification theorem for closed surfaces, he has mentioned an example that a sphere with one handle and one Möbius strip glued is homeomorphic to a sphere with three Möbius strips glued.
I am not able to see this. I know that to prove the above is to say that a torus with a Möbius strip glued is homeomorphic to a Klein bottle with a Möbius strip glued. How do I prove this? Or how do I at least convince myself that this is the case, in case I don't yet have the tools to prove it.