as Bill pointed it out, a Kbottle can be cut into two Mstrips, but they are really the same thing, if the ideal of "compactness" is modified. that is, there is a standard way to parameterize the Mstrip, which arbitrarily limits it to being a strip, half a unit wide on both sides of the generating circle.
if it is an infinite surface, it has an irreducible self-intersection, same as the Kbottle, although this is usually handwaved-away with some stuff about "4dness."
anyway, you can "do" an Matrip with an old bike tube, in more than one way. or, maybe it's the Kbottle manifestation.