  The evolution of relative canonical helicity is examined in the two-fluid
magnetohydrodynamic formalism. Canonical helicity is defined here as the
helicity of the plasma species' canonical momentum. The species' canonical
helicity are coupled together and can be converted from one into the other
while the total gauge-invariant relative canonical helicity remains globally
invariant. The conversion is driven by enthalpy differences at a surface common
to ion and electron canonical flux tubes. The model provides an explanation for
why the threshold for bifurcation in counter-helicity merging depends on the
size parameter. The size parameter determines whether magnetic helicity
annihilation channels enthalpy into the magnetic flux tube or into the
vorticity flow tube components of the canonical flux tube. The transport of
relative canonical helicity constrains the interaction between plasma flows and
magnetic fields, and provides a more general framework for driving flows and
currents from enthalpy or inductive boundary conditions.
