Flips in edge-labelled pseudo-triangulations

Given a set of n points in the plane, we show that O(n2) 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(nlog⁡c+hlog⁡h) flips, where c is the number of convex layers and h is the number of points on the convex hull.