Interleaving Mayer–Vietoris spectralsequences

We discuss the Mayer-Vietoris spectral sequence as an invariant in the context of persistent homology.In particular, we introduce the notion of "-acyclic carriers and "-acyclic equivalences between filtered regular CW-complexes and study stability conditions for the associated spectral sequences.We also look at the Mayer-Vietoris blowup complex and the geometric realization, finding stability properties under compatible noise; as a result we prove a version of an approximate nerve theorem.Adapting work by Serre, we find conditions under which "-interleavings exist between the spectral sequences associated to two different covers. 55N31, 55T99