An inverting mechanism for a glassware forming machine of the type comprising: a supporting structure; a shaft horizontally located on upper part of the supporting structure to rotate on its own axis, said shaft including a longitudinal central passage with a closed end and an open end and, at least one exit passage (74, 76) connecting the central part of the central passage towards the surface part of the shaft, for the introduction of a fluid under pressure; drive means coupled to the shaft to provide rotational movement to the shaft, on its own horizontal axis, to the left or to the right; at least one cylindrical body (82, 84) having a front face (110, 112) and a rear face (110A, 112A), this cylindrical body (82, 84) has a longitudinal hole (86, 88) in an eccentric reference axis, this cylindrical body (82, 84) being fixedly coupled to the shaft through its longitudinal hole (86, 88), in an eccentric position; at least one hollow cylinder (90, 92) coupled to each cylindrical body (82, 84), each hollow cylinder (90, 92) having supports (S1, S2) coupled on its outer part, which are connected to neck ring holder arms so that, by means of a first sliding movement of the hollow cylinder (90, 92) on the cylindrical body (82, 84), provides a lateral movement to the right or to the left to open and close the neck ring holder arm supports in parallel and, by means of a rotational movement, to move the neck ring holder arms with a 180° movement from a parison mold to a final blow mold; at least one cover (94, 96) with one hole (98, 100) in eccentric position, said cover (94, 96) being coupled by means of its eccentric hole (98, 100) to a section of the shaft and, by its periphery, being fixedly coupled and coinciding with one end of each hollow cylinder (90, 92), said cover (94, 96) being sliding together with each hollow cylinder (90, 92), wherein the front face (110, 112) of the cylindrical body (82, 84) and the sliding cover (94, 96) form an intermediate chamber (102, 104) for the inlet of a fluid under pressure through the longitudinal central passage and exit passages (74, 76) of the shaft, said chambers (102, 104) being in coincidence with exit passages (74, 76) of the shaft; at least one adjustment element (114, 116) attached to the shaft and located in facing position with the sliding cover (94, 96), said coupling of the adjustment element (114, 116) and the sliding cover (94, 96), forming a hollow internal space therebetween; and, retracting means (130, 132) located in said hollow internal space to provide a retracting motion to said hollow cylinder (90, 92) and to said cover (94, 96) sliding on said shaft, at the time of interrupting the fluid pressure, to parallelly close the supports of the neck ring holder arms. a supporting structure; a shaft horizontally located on upper part of the supporting structure to rotate on its own axis, said shaft including a longitudinal central passage with a closed end and an open end and, at least one exit passage (74, 76) connecting the central part of the central passage towards the surface part of the shaft, for the introduction of a fluid under pressure; drive means coupled to the shaft to provide rotational movement to the shaft, on its own horizontal axis, to the left or to the right; at least one cylindrical body (82, 84) having a front face (110, 112) and a rear face (110A, 112A), this cylindrical body (82, 84) has a longitudinal hole (86, 88) in an eccentric reference axis, this cylindrical body (82, 84) being fixedly coupled to the shaft through its longitudinal hole (86, 88), in an eccentric position; at least one hollow cylinder (90, 92) coupled to each cylindrical body (82, 84), each hollow cylinder (90, 92) having supports (S1, S2) coupled on its outer part, which are connected to neck ring holder arms so that, by means of a first sliding movement of the hollow cylinder (90, 92) on the cylindrical body (82, 84), provides a lateral movement to the right or to the left to open and close the neck ring holder arm supports in parallel and, by means of a rotational movement, to move the neck ring holder arms with a 180° movement from a parison mold to a final blow mold; at least one cover (94, 96) with one hole (98, 100) in eccentric position, said cover (94, 96) being coupled by means of its eccentric hole (98, 100) to a section of the shaft and, by its periphery, being fixedly coupled and coinciding with one end of each hollow cylinder (90, 92), said cover (94, 96) being sliding together with each hollow cylinder (90, 92), wherein the front face (110, 112) of the cylindrical body (82, 84) and the sliding cover (94, 96) form an intermediate chamber (102, 104) for the inlet of a fluid under pressure through the longitudinal central passage and exit passages (74, 76) of the shaft, said chambers (102, 104) being in coincidence with exit passages (74, 76) of the shaft; at least one adjustment element (114, 116) attached to the shaft and located in facing position with the sliding cover (94, 96), said coupling of the adjustment element (114, 116) and the sliding cover (94, 96), forming a hollow internal space therebetween; and, retracting means (130, 132) located in said hollow internal space to provide a retracting motion to said hollow cylinder (90, 92) and to said cover (94, 96) sliding on said shaft, at the time of interrupting the fluid pressure, to parallelly close the supports of the neck ring holder arms.