  The simultaneous embeddings of an axion state and a seesaw mechanism within
the SU(5) Grand Unification Theory, both minimal and flipped, are
systematically studied. It is shown that whenever B-L is active as a global
symmetry, the PQ charges of the fermions are ambiguous. Various realizations of
the seesaw mechanism are then found to differ only in the way this ambiguity is
resolved. But since the ambiguity is unphysical, all these models are thereby
predicted to be equivalent, in the sense that the axion phenomenology is
identical at the low energy scale.
