An anvil assembly is described. The anvil assembly includes including an axis with a proximal and a distal portion, an anvil associated to the distal portion of the axis formed by a central portion and at least a remote rotating portion and a system for reducing the encumbrance of the assembly of the anvil and relative restoring of such encumbrance. This is possible thanks to a half-automatic system specifically activated by the user of the surgical instrument and/or by an automatic system integrated in the system for opening and closing the surgical instrument without the need of activating any specific mechanism. The reduction and the restoring of the anvil size is an advantage during the insertion and the removal of the anvil into and from the organ of the patient.