Consider the equivalence relation ~ on $\displaystyle \mathbb{R}^2$.

$\displaystyle (x,y) \sim (x,y+1)$ and $\displaystyle (x,y) \sim (x+1,-y)$

The quotient $\displaystyle K = \mathbb{R}^2/ \sim$ is the Klein Bottle. Show that the quotient map $\displaystyle p: \mathbb{R}^2\rightarrow K$ is a covering.

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

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?