Suppose we delete two points from the complex plane, call them $p$ and $q$. Call the resulting space $X$. We're looking for notation for paths from a point $a \in X$ to a point $b \in X$ that's specific enough that we know exactly how we're twisting around the points $p$ and $q$, to get from $a$ to $b$, but not so specific that we have to actually define the path up to equality.
Question. Is there good notation for this kind of thing, where we wish to denote paths up to homotopy only?
I'm interested both in the specific case where all we're dealing with is the plane minus a few points, and also in the more general case where we're dealing with an arbitrary manifold.
This could be useful for denoting contour integrals, for example.