*Properness properties of the bending map*

**Abstract:**
In this talk, I will explain some links between the convergence of a sequence of
geometrically finite hyperbolic metrics on the interior of a compact 3-manifold
and the behaviour of the bending geodesic measured laminations of the convex
cores of these metrics. I will emphasize on sequences of metrics such that the
limit has more rank one cusps than the elements of the sequence