  We demonstrate that an excision property holds for persistent homology
groups. This property holds for a large class of filtrations, and in fact we
show that given any filtration on a larger space, we can extend it to a
filtration of two subspaces which guarantees that the excision property holds
for the triple. This method also applies to the Mayer-Vietoris sequence in
persistent homology introduced by DiFabio and Landi in 2011, extending their
results to a much larger class of filtrations.
