Resolvent $H_{-1}$ norms with respect to simple exclusion processes
play an important role in many problems with respect
to additive functionals, tagged particles, and hydrodynamics,
among other concerns. Here, general translation-invariant
finite-range simple exclusion processes with and
without a distinguished particle are considered.
For the standard system of indistinguishable particles,
it is proved that the corresponding $H_{-1}$ norms are equivalent, in a sense,
to the $H_{-1}$ norms of a nearest-neighbor system.
The same result holds for systems with
a distinguished particle in dimensions
$d\geq 2$. However, in dimension $d=1$,
this equivalence does not hold.
An application of the $H_{-1}$ norm equivalence to additive
functional variances is also given.