Exact results for state-to-state transition probabilities in the   multistate Landau-Zener model by non-stationary perturbation theory
  Multistate generalizations of Landau-Zener model are studied by summing entire series of perturbation theory. A new technique for analysis of the series is developed. Analytical expressions for probabilities of survival at the diabatic potential curves with extreme slope are proved. Degenerate situations are considered when there are several potential curves with extreme slope. New expressions for some state-to-state transition probabilities are derived in degenerate cases. 
M.V.Volkov and V.N.Ostrovsky