  We show that the phenomenology of isospin effects on heavy ion reactions at
intermediate energies (few AGeV range) is extremely rich and can allow a
``direct'' study of the covariant structure of the isovector interaction in the
hadron medium. We work within a relativistic transport frame, beyond a cascade
picture, consistently derived from effective Lagrangians, where isospin effects
are accounted for in the mean field and collision terms. Rather sensitive
observables are proposed from collective flows (``differential'' flows) and
from pion/kaon production ($\pi^-/\pi^+$, $K^0/K^+$ yields). For the latter
point relevant non-equilibrium effects are stressed. The possibility of the
transition to a mixed hadron-quark phase, at high baryon and isospin density,
is finally suggested. Some signatures could come from an expected ``neutron
trapping'' effect.
