  Let $\overline{M}$ be a compact smoothly stratified pseudo-manifold endowed
with a wedge metric $g$. Let $\overline{M}_\Gamma$ be a Galois
$\Gamma$-covering. Under additional assumptions on $\overline{M}$, satisfied
for example by Witt pseudo-manifolds, we show that the $L^2$-Betti numbers and
the Novikov-Shubin invariants are well defined. We then establish their
invariance under a smoothly stratified, strongly stratum preserving homotopy
equivalence, thus extending results of Dodziuk, Gromov and Shubin to these
pseudo-manifolds.
