Nuclear masses are one of the key ingredients of nuclear physics that go into astrophysical simulations of the $r$ process. Nuclear masses effect $r$-process abundances by entering into calculations of Q-values, neutron capture rates, photo-dissociation rates, beta-decay rates, branching ratios and the properties of fission. Most of the thousands of short-lived neutron-rich nuclei which are believed to participate in the $r$ process lack any experimental verification, thus the identification of the most influential nuclei is of paramount importance. We have conducted mass sensitivity studies near the $N=82$ closed shell in the context of a main $r$-process. Our studies take into account how an uncertainty in a single nuclear mass propagates to influence the relevant quantities of neighboring nuclei and finally to $r$-process abundances. We identify influential nuclei in various astrophysical conditions using the FRDM mass model. We show that our conclusions regarding these key nuclei are still retained when a superposition of astrophysical trajectories is considered.
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