Flips in Edge-Labelled Pseudo-Triangulations

We show that $O(n^2)$ exchanging flips suffice to transform any edge-labelled pointed pseudo-triangulation into any other with the same set of labels. By using insertion, deletion and exchanging flips, we can transform any edge-labelled pseudo-triangulation into any other with $O(n log c + h log h)$ flips, where $c$ is the number of convex layers and $h$ is the number of points on the convex hull.