Mobius strips, are generally held to have only one side - if one marks a place on the strip and on what looks like the other side then a pencil can draw a line between these two points without ever leaving the surface of the strip.
Technically this property is called non-orientability; and what we've done in the above demonstration is show that both 'sides' are path-connected.
So our intuition is shown to be limited and a little foolish.
However, one can as why then does it look as though it has two sides; a little thought shows that it is because we examine locally; in the same way that the earth looks flat, but in fact is round, and we resolve this tension by saying that the earth is locally flat; similarly we can say that the mobius strip is locally two-sided but not so globally.
(Now if the default adjective applied to the concept is local rather than global we could just simply say that the mobius strip is two-sided).
So, can we say that the Mobius strip has a front and back, despite all the write-ups it has had, by adding 'locally' as a qualifier?