  We establish a Cheeger-Muller theorem for unimodular representations
satisfying a Witt condition on a noncompact manifold with cusps. This class of
spaces includes all non-compact hyperbolic spaces of finite volume, but we do
not assume that the metric has constant curvature nor that the link of the cusp
is a torus. We use renormalized traces in the sense of Melrose to define the
analytic torsion and we relate it to the intersection R-torsion of Dar of the
natural compactification to a stratified space. Our proof relies on our recent
work on the behavior of the Hodge Laplacian spectrum on a closed manifold
undergoing degeneration to a manifold with fibered cusps.
