Why is a cylinder and a Mobius strip NOT topologically equivalent?

A cylinder and a Möbius strip are not topologically equivalent because they have different properties regarding their boundaries and orientability. A cylinder has two distinct edges (boundaries) and is orientable, meaning it is possible to distinguish a "left" side from a "right" side. In contrast, a Möbius strip has only one edge and is non-orientable, meaning if you travel along its surface, you can end up on the "opposite" side without ever crossing an edge. These fundamental differences in structure prevent the two shapes from being transformed into one another through continuous deformation.