  We introduce spectral flow techniques to explain why the Fermi arcs of Weyl
semimetals are topologically protected against boundary condition changes and
perturbations. We first analyse the topology of a certain universal space of
self-adjoint half-line massive Dirac Hamiltonians, and then exploit its
non-trivial and homotopy invariant spectral flow structure by pulling it back
to generic Weyl semimetal models. The homological perspective of using Dirac
strings/Euler chains as global topological invariants of Weyl semimetals/Fermi
arcs, is thereby analytically justified.
