Mobile equipment for suctioning and filtering particulate material from a flow comprising air and non-volatile particulate material, wherein the equipment comprises at least one first filter stage (12), having at least one first outlet (12b) for conveying the treated flow downstream towards at least one suction pump (14), and at least one second filter stage (13) arranged in cascade at the least one first filter stage (12), the first outlet (12b) of the first filter stage (12) being connected to the inlet (13a) of the second filter stage (13), wherein downstream of the at least one suction pump (14) there is provided a first group (15) for monitoring the residual particulate material exiting from the at least one suction pump (14), the first monitoring group (15) being connected to processing means (16) for controlling - opening and closing - a pair of valves (17,18) for selectively directing a flow exiting from the at least one suction pump (14) towards an additional filter stage (19) arranged downstream of the first monitoring group (15), or directly towards an outlet for release into the open air.