High energy Heavy Ion Collisions (HIC) are studied in order to access nuclear matter properties at high density. Particular attention is paid to the selection of observables sensitive to the poorly known symmetry energy at high baryon density, of large fundamental interest, even for the astrophysics implications. Using fully consistent transport simulations built on effective theories we test isospin observables ranging from nucleon/cluster emissions to collective flows (in particular the elliptic, squeeze out, part). The effects of the competition between stiffness and momentum dependence of the Symmetry Potential on the reaction dynamics are thoroughly analyzed. In this way we try to shed light on the controversial neutron/proton effective mass splitting at high baryon and isospin densities. New, more exclusive, experiments are suggested.
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