  A time-dependent two interacting spin-qutrit model is analysed and solved.
The two interacting qutrits are subjected to a longitudinal field linearly
varying over time as in the Landau-Majorana-St\"uckelberg-Zener (LMSZ)
scenario. Although a transverse field is absent, we show the occurrence of LMSZ
transitions assisted by the coupling between the two spin-qutrits. Such a
physical effects permits to estimate experimentally the coupling strength
between the spins and allows the generation of entangled states of the two
qutrits by appropriately setting the slope of the ramp. Furthermore, the
possibility of local and non-local control as well as the existence of dark
states of the two qutrits have been brought to light. Effects stemming from a
noisy surrounding environment are also taken into account by introducing a
random fluctuating field component as well as non-Hermitian terms in the
Hamiltonian model.
