A cover for a storage battery, comprising: - a substantially planar main closure element, suitable for closing a battery case, in which a plurality of filling holes are provided, intended to provide access to the inside of the battery case, - a secondary closure element, mounted on the main element for closing the holes of the main element of the cover, and - at least one conduit, provided in at least one of said main and secondary elements and in flow communication with said holes, and which is arranged for discharging the gases generated inside the case of said battery, wherein said main and secondary elements together form a box-like structure (3, 4) defining a chamber in flow communication with the holes, and inside which the main and secondary elements are connected to each other by a plurality of baffles extending substantially perpendicularly with respect to the plane of extension of the main element, and arranged in such a way as to define a labyrinth which connects said holes in the main element to said gas discharge conduit; wherein said plurality of baffles comprises a plurality of transverse walls interposed between each hole and the adjacent hole, and which extend so as to subdivide the chamber into a plurality of sub-chambers (6a, 6b, 6c), each sub-chamber (6a, 6b, 6c) thus containing a respective hole of the plurality of holes, and wherein the sub-chambers are individually in flow communication with a collecting channel which communicates with the gas discharge conduit and comprises a first and a second longitudinal channel portion (41a, 41b), which extend along opposite sides of the chamber, and a transverse channel portion which interconnects said first and second longitudinal channel portions, said first longitudinal channel portion providing flow communication with said sub-chambers and said second longitudinal channel portion providing flow communication with the gas discharge conduit via an outlet chamber which communicates with the second longitudinal channel portion, a connecting conduit and a winding flow path being formed inside each sub-chamber, wherein the connecting conduit is arranged alongside the respective hole and opens directly onto the first channel portion of the collecting channel, and the winding flow path places the connecting conduit in indirect flow communication with the respective hole, characterized in that the sub-chambers are individually in flow communication with the collecting channel, and the transverse channel portion of the collecting channel extends along the centre line of the chamber. - a substantially planar main closure element, suitable for closing a battery case, in which a plurality of filling holes are provided, intended to provide access to the inside of the battery case, - a secondary closure element, mounted on the main element for closing the holes of the main element of the cover, and - at least one conduit, provided in at least one of said main and secondary elements and in flow communication with said holes, and which is arranged for discharging the gases generated inside the case of said battery, the sub-chambers are individually in flow communication with the collecting channel, and the transverse channel portion of the collecting channel extends along the centre line of the chamber.