Sorry, I misuse the concept of quasi-isometry, I mean almost isometry(also called a Hausdorff approximation).

As we known, isometric Riemann manifolds have the same spectrum of Laplace-Beltrami. And it defined a class of isospectral manifolds which is a highly identical signature of manifold. However, in application, almost-isometry is more useful. Does anyone provide me an overview or reference of the relationship between spectrum and almost-isometry?