  We provide new vanishing and glueing results for relative simplicial volume,
following up on two current themes in bounded cohomology: The passage from
amenable groups to boundedly acyclic groups and the use of equivariant
topology.
  More precisely, we consider equivariant nerve pairs and relative classifying
spaces for families of subgroups. Typically, we apply this to uniformly
boundedly acyclic families of subgroups. Our methods also lead to vanishing
results for $\ell^2$-Betti numbers of aspherical CW-pairs with small relative
amenable category and to a relative version of a result by Dranishnikov and
Rudyak concerning mapping degrees and the inheritance of freeness of
fundamental groups.

Algebraic Topology;Geometric Topology