  We present two results related to magnetized Vlasov equations. Our first
contribution concerns the stability of solutions to the magnetized
Vlasov-Poisson system with a non-uniform magnetic field using the optimal
transport approach introduced by Loeper [24]. We show that the extra magnetized
terms can be suitably controlled by imposing stronger decay in velocity on one
of the distribution functions, illustrating how the external magnetic field
creates anisotropy in the evolution. This allows us to generalize the classical
2-Wasserstein stability estimate by Loeper [24, Theorem 1.2] and the recent
stability estimate using a kinetic Wasserstein distance by Iacobelli [20,
Theorem 3.1] to the magnetized Vlasov-Poisson system. In our second result, we
extend the improved Dobrushin estimate by Iacobelli [20, Theorem 2.1] to the
magnetized Vlasov equation with a uniform magnetic field.
