  In this paper we give a complete description of the set of discrete faithful
representations SH(M) uniformizing a compact, orientable, hyperbolizable
3-manifold M with incompressible boundary, equipped with the strong topology,
with the description given in term of the end invariants of the quotient
manifolds. As part of this description, we introduce coordinates on SH(M) that
extend the usual Ahlfors-Bers coordinates. We use these coordinates to show the
local connectivity of SH(M) and study the action of the modular group of M on
SH(M).
