Multilevel resistance states in silver-manganite interfaces are studied both experimentally and through a realistic model that includes as a main ingredient the oxygen vacancies diffusion under applied electric fields. The switching threshold and amplitude studied through hysteresis switching loops are found to depend critically on the initial state. The associated vacancy profiles further unveil the prominent role of the effective electric field acting at the interfaces. While experimental results validate main assumptions of the model, the simulations allow to disentangle the microscopic mechanisms behind the resistive switching in metal-transition metal oxide interfaces.