  The effect of possible in-medium modifications of nucleon-nucleon ($NN$)
cross sections on particle production is investigated in heavy ion collisions
($HIC$) at intermediate energies. In particular, using a fully covariant
relativistic transport approach, we see that the density dependence of the {\it
inelastic} cross sections appreciably affects the pion and kaon yields and
their rapidity distributions. However, the $(\pi^{-}/\pi^{+})$- and
$(K^{0}/K^{+})$-ratios depend only moderately on the in-medium behavior of the
inelastic cross sections. This is particularly true for kaon yield ratios,
since kaons are more uniformly produced in high density regions. Kaon
potentials are also suitably evaluated in two schemes, a chiral perturbative
approach and an effective meson-quark coupling method, with consistent results
showing a similar repulsive contribution for $K^{+}$ and $K^{0}$. As a
consequence we expect rather reduced effects on the yield ratios. We conclude
that particle ratios appear to be robust observables for probing the nuclear
equation of state ($EoS$) at high baryon density and, particularly, its
isovector sector.
