  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.
