Stability of $L^2-$invariants on stratified spaces

Let $\bar{M}$ be a compact smoothly stratified pseudo-manifold endowed with a wedge metric $g$. Let ${\bar{M}}_{\mathrm{\Gamma }}$ be a Galois $\mathrm{\Gamma }$-covering. Under additional assumptions on $\bar{M}$, 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.