  We show how non-reciprocal ferromagnetic interactions between neighbouring
planar spins in two dimensions, affect the behaviour of topological defects.
Non-reciprocity is introduced by weighting the coupling strength of the
two-dimensional XY model by an anisotropic kernel. As a consequence, in
addition to the topological charge $q$, the actual shape of the defects becomes
crucial to faithfully describe their dynamics. Non-reciprocal coupling twists
the spin field, selecting specific defect shapes, dramatically altering the
pair annihilation process. Defect annihilation can either be enhanced or
hindered, depending on the shape of the defects concerned and the degree of
non-reciprocity in the system. We introduce a continuous description -- for
which the phenomenological coefficients can be explicitly written in terms of
the microscopic ones -- that captures the behaviour of the lattice model.
