  Quantum vortices are often endowed with an effective inertial mass, due, for
example, to massive particles in their cores. Such "massive vortices" display
new phenomena beyond the standard picture of superfluid vortex dynamics, where
the mass is neglected. In this work, we demonstrate that massive vortices are
allowed to collide, as opposed to their massless counterparts. We propose a
scheme to generate controllable, repeatable, deterministic collisional events
in pairs of quantum vortices. We demonstrate two mass-driven fundamental
processes: (i) the annihilation of two counter-rotating vortices and (ii) the
merging of two co-rotating vortices, thus pointing out new mechanisms
supporting incompressible-to-compressible kinetic energy conversion, as well as
doubly-quantized vortices stabilization in flat superfluids.
