Consider the equivalence relation ~ on .

and

The quotient is the Klein Bottle. Show that the quotient map is a covering.

Dont really know how to start I know I need to find an open cover of wherethe preimage of each under p is a disjoint union of open sets of which each is homeomorphic to .

Any hints are welcome. I basically dont see how this equivalence relation works. I know the Klein Bottle as quotient of I^2 with (0,y) ~ (1,y) and (x,0) ~ (1-x,1). Is this somehow related to this task?