  A distance between von Neumann algebras is introduced, depending on a further
norm inducing the $w^*$-topology on bounded sets. Such notion is related both
with the Gromov-Hausdorff distance for quantum metric spaces of Rieffel and
with the Effros-Marechal topology on the von Neumann algebras acting on a
Hilbert space. This construction is tested on the local algebras of free
quantum fields endowed with norms related with the Buchholz-Wichmann nuclearity
condition, showing the continuity of such algebras w.r.t. the mass parameter.
