The figure gives a 4-sheeted covering map from the torus to the Klein bottle. I am trying to show that this covering map is not normal, but I got stuck. (Actually I am solving an exercise to construct a non-normal covering of the Klein bottle by a torus.) Is there an efficient way to show that this covering is not normal?
Edit: Is this actually a covering map? If we let $a$ denote the loop on the Klein bottle given by the arrow $>>$, then I can't see it's lift starting at the corner point of the torus.