  Using a transport model coupled with a phase-space coalescence after-burner
we study the triton-$^3$He ratio, relative and differential transverse flows in
semi-central $^{132}Sn+^{124}Sn$ reactions at a beam energy of 400 MeV/A. The
neutron-proton ratio, relative and differential flows are also discussed as a
reference. We find that similar to the neutron-proton pairs the triton-$^3$He
pairs also carry interesting information about the density dependence of the
nuclear symmetry energy. Moreover, the nuclear symmetry energy affects more
strongly the t-$^3$He relative and differential flows than the $\pi^-/\pi^+$
ratio in the same reaction. The t-$^3$He relative flow can be used as a
particularly powerful probe of the high-density behavior of the nuclear
symmetry energy.
