  We derive the expression of the abelian axial anomaly in the so-called
multi-Weyl and triple-point crossing semimetals. No simplifying restrictions
are assumed on the symmetry of the spectrum. Three different computation
methods are considered: the perturbative quantum field theory procedure which
is based on the evaluation of the one-loop Feynman diagrams, the
Nielsen-Ninomiya method, and the Atiyah-Singer index argument. It is shown that
the functional form of the axial anomaly does not depend on the Lorentz
symmetry, but it is determined by the gauge structure group. We discuss the
stability of the anomaly - stemming from the quantisation of the anomaly
coefficient - under smooth modifications of the lagrangian parameters.

Strongly Correlated Electrons;Mesoscale and Nanoscale Physics;Quantum Gases;High Energy Physics - Theory;Quantum Physics