It is disclosed a device (1) for altering the storage capacity of a tubular mesh bag of heat sealable material during the manufacture thereof and the bag (15) obtained from its using. The device comprises an expansion core (2) to which the tubular mesh is peripheral, which is essentially oblong and will be inserted vertically inside the tubular mesh, thus determining two from faces (21) and two side faces of said mesh as it passes over the expansion core. The device has a mechanism for inserting, in a variable way as the mesh passes over the expansion core, sections of the peripheral tubular mesh into it, thus accumulating a greater or smaller quantity of mesh in each longitudinal section of mesh corresponding with one bag unit.