  Two Riemannian manifolds are called eigenvalue equivalent when their sets of
eigenvalues of the Laplace-Beltrami operator are equal (ignoring
multiplicities). They are (primitive) length equivalent when the sets of
lengths of their (primitive) closed geodesics are equal. We give a general
construction of eigenvalue equivalent and primitive length equivalent
Riemannian manifolds. For example we show that every finite volume hyperbolic
$n$--manifold has pairs of eigenvalue equivalent finite covers of arbitrarily
large volume ratio. We also show the analogous result for primitive length
equivalence.
