  A three-state system subjected to a time-dependent Hamiltonian whose bare
energies undergo one or more crossings, depending on the relevant parameters,
is considered, also taking into account the role of dissipation in the
adiabatic following of the Hamiltonian eigenstates. Depending on the fact that
the bare energies are equidistant or not, the relevant population transfer
turns out to be very sensitive to the environmental interaction or relatively
robust. The physical mechanisms on the basis of this behavior are discussed in
detail.
