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

Bounded acyclicity and relative simplicial volume