  By means of $ab \ initio$ band structure methods and model Hamiltonians we
investigate the electronic, spin and topological properties of four
monopnictides crystallizing in body centered tetragonal structure. We show that
the Weyl bands around a Weyl point W1 or W2 possess a strong anisotropy and
tilt of the accompanying Dirac cones. These effects are larger for W2 nodes
than for W1 ones. The node tilts and positions in energy space significantly
influence the density of states of single-particle Weyl excitations. The node
anisotropies destroy the conventional picture of (anti)parallel spin and wave
vector of a Weyl fermion. This also holds for the Berry curvature around a
node, while the monopole charges are independent as integrated quantities. The
pairing of the nodes strongly modify the spin texture and the Berry curvature
for wave vectors in between the two nodes. Spin components may change their
orientation. Integrals over planes perpendicular to the connection line yield
finite Zak phases and winding numbers for planes between the two nodes, thereby
indicating the topological character.
