  We have performed for the first time a complete $r$-process mass sensitivity
study in the $N=82$ region. We take into account how an uncertainty in a single
nuclear mass propagates to influence important quantities of neighboring
nuclei, including Q-values and reaction rates. We demonstrate that nuclear mass
uncertainties of $\pm0.5$ MeV in the $N=82$ region result in up to an order of
magnitude local change in $r$-process abundance predictions. We identify key
nuclei in the study whose mass has a substantial impact on final $r$-process
abundances and could be measured at future radioactive beam facilities.
