Pump comprising - a pump casing defining internally a working chamber, - an impeller accommodated in the working chamber, - a shaft which is rotatably mounted about an axis of rotation (x) and on which the impeller is mounted so as to be drivingly connected for rotation therewith, and - a cover fixed on the front side of the pump casing to close the working chamber, wherein the working chamber is delimited radially by a lateral surface having a profile with a variable radius with respect to said axis of rotation (x), and wherein the impeller comprises a hub and a plurality of elastically flexible blades which extend radially outwards from the hub and are configured to cooperate with the lateral surface of the work chamber so as to be alternately deflected and released when the impeller is driven by the shaft into rotation about said axis of rotation (x), wherein the cover has, in a lower region thereof, a drain hole for allowing liquid contained inside the working chamber to flow out of the same, and wherein the pump further comprises closing means (50, 52, 54, 56, 58, 60) selectively operable to close or open said drain hole to prevent or allow, respectively, the flow of the liquid out of the working chamber through said drain hole, characterized in that the cover has on an inner side thereof, in the area of said drain hole, a slot having a width larger than the diameter of said drain hole and larger than the thickness of the blades of the impeller, and in that the inner side of the cover has a groove arranged to put spaces of the working chamber enclosed between pairs of adjacent blades of the impeller into communication with each other. - a pump casing defining internally a working chamber, - an impeller accommodated in the working chamber, - a shaft which is rotatably mounted about an axis of rotation (x) and on which the impeller is mounted so as to be drivingly connected for rotation therewith, and - a cover fixed on the front side of the pump casing to close the working chamber, wherein the working chamber is delimited radially by a lateral surface having a profile with a variable radius with respect to said axis of rotation (x), and wherein the impeller comprises a hub and a plurality of elastically flexible blades which extend radially outwards from the hub and are configured to cooperate with the lateral surface of the work chamber so as to be alternately deflected and released when the impeller is driven by the shaft into rotation about said axis of rotation (x), wherein the cover has, in a lower region thereof, a drain hole for allowing liquid contained inside the working chamber to flow out of the same, and wherein the pump further comprises closing means (50, 52, 54, 56, 58, 60) selectively operable to close or open said drain hole to prevent or allow, respectively, the flow of the liquid out of the working chamber through said drain hole, characterized in that the cover has on an inner side thereof, in the area of said drain hole, a slot having a width larger than the diameter of said drain hole and larger than the thickness of the blades of the impeller, and in that the inner side of the cover has a groove arranged to put spaces of the working chamber enclosed between pairs of adjacent blades of the impeller into communication with each other.