  The manipulation and movement of Dirac points in the Brillouin zone by the
electron-electron interaction is considered within leading order perturbation
theory. At the merging point, an infinitesimal interaction is shown to cause
opening of the gap or splitting of the Dirac points, depending on the inter- or
intrasublattice nature of the merging and the sign of the interaction. The
topology of the spectrum can therefore be efficiently changed by simply tuning
the interaction between particles, as opposed to the usual careful band
structure engineering. This is illustrated around the merging transition of
one, two, and three dimensional Dirac-Weyl fermions. A simple Weyl-like
Hamiltonian that describes the quadratic band-crossing in three dimensions is
also proposed, and its stability under interactions is addressed.
