  In this paper we study the ergodic theory of the geodesic flow on negatively
curved geometrically finite manifolds. We prove that the measure theoretic
entropy is upper semicontinuous when there is no loss of mass. In case we are
losing mass, the critical exponents of parabolic subgroups of the fundamental
group have a significant meaning. More precisely, the failure of
upper-semicontinuity of the entropy is determinated by the maximal parabolic
critical exponent. We also study the pressure of positive H\"older continuous
potentials going to zero through the cusps. We prove that the pressure map
$t\mapsto P(tF)$ is differentiable until it undergoes a phase transition, after
which it becomes constant. This description allows, in particular, to compute
the entropy at infinity of the geodesic flow.
