It is well known that plane is universal cover of Torus and Klein Bottle. If we consider the map $\phi:\mathbb{R}^2\rightarrow S^1\times S^1$, defined as $\phi(x,y)=(e^{2i\pi x},e^{2i\pi y})$, then $\phi$ becomes covering map for Torus.
In a similar manner how we can find a covering map for Klein bottle.
I have seen questions like this The double cover of Klein bottle , but did not find the appropriate thing. Please help me thanking you.