  Persistent homology is a popular data analysis technique that is used to
capture the changing topology of a filtration associated with some simplicial
complex $K$. These topological changes are summarized in persistence diagrams.
We propose two contraction operators which when applied to $K$ and its
associated filtration, bound the perturbation in the persistence diagrams. The
first assumes that the underlying space of $K$ is a $2$-manifold and ensures
that simplices are paired with the same simplices in the contracted complex as
they are in the original. The second is for arbitrary $d$-complexes, and bounds
the bottleneck distance between the initial and contracted $p$-dimensional
persistence diagrams. This is accomplished by defining interleaving maps
between persistence modules which arise from chain maps defined over the
filtrations. In addition, we show how the second operator can efficiently
compose across multiple contractions. We conclude with experiments
demonstrating the second operator's utility on manifolds.
