  Because the Peccei-Quinn (PQ) symmetry has to be anomalous to solve the
strong CP puzzle, some colored and chiral fermions have to transform
non-trivially under this symmetry. But when the SM fermions are charged, as in
the PQ or DFSZ models, this symmetry ends up entangled with the SM global
symmetries, baryon (B) and lepton (L) numbers. This raises several questions
addressed in this paper. First, the compatibility of axion models with some
explicit B and/or L violating effects is analyzed, including those arising from
seesaw mechanisms, electroweak instanton interactions, or explicit B and L
violating effective operators. Second, how many of these effects can be
simultaneously present is quantified, along with the consequences for the axion
mass and vacuum alignment if too many of them are introduced. Finally, large
classes of B and/or L violating interactions without impact on axion
phenomenology are identified, like for example the various implementations of
the type I and II seesaw mechanisms in the DFSZ context.
