This is a question from Needham's "Visual Complex Analysis". Kindly refer to the photo below.
Let $K$ be a line moving downwards. The book says that if we move a point $r$ from the left to the right of $K$, we decrease $v(K,r)$ by $1$.
But in the diagram, $K$ seems to be "looping" around $r$ as it moves from left to right. Why does the diagram not simply show two diagrams- one in which $r$ is to the left of $K$ and another in which $r$ is to the right? I don't get the point of this diagram.
I am thinking it is to show the intuition for K and L together (in the right diagram) contributing the same winding number as K alone (in the left diagram), because the pinch point might be somewhat non-intuitive to some readers, and a continuous deformation to this state might make it more clear.