A rotary blowing machine for thermoplastic material containers, adapted to rotate about a rotation axis, comprising a plurality of blowing molds, each having a first half-mold defined front half mold in the sense of rotation of the blowing machine, a second half-mold, defined rear half-mold in the sense of rotation of the blowing machine, the first half-mold and the second half-mold being closable as a book around a hinge axis lying on a symmetry plane of the mold coinciding with a radial plane passing through the rotation axis, each blowing mold comprising at least one cam track, an opening and closing mechanism adapted to allow the extraction of blown containers and the insertion of preforms to be blown, having - a first shaft (15, 15'), pivoting around an axis (D, B') thereof, parallel to the hinge axis, - a second shaft (16, 16'), pivoting around an axis (E, C') thereof, parallel to the hinge axis, - at least one first crank and at least one second crank integrally fixed to the first shaft, the at least one second crank having an end to which a first cam follower is fixed, and at least one third crank and at least one fourth crank integrally fixed to the second shaft, the at least one fourth crank (8, 8') having an end to which a second cam follower is fixed; or at least one first crank integrally fixed to the first shaft and a first cam follower hinged to said first shaft, and at least one second crank integrally fixed to the second shaft and a second cam follower hinged to said second shaft; - at least one first connecting rod (3, 3') hinged at a first end thereof to the first half-mold and constrained with a second end thereof to the first shaft (15, 15'), - at least a second connecting rod (4, 4') hinged at a first end thereof to the second half-mold and constrained with a second end thereof to the second shaft (16, 16'), wherein each blowing mold is provided with a single first cam track, and wherein the first cam follower (17, 17') and the second cam follower (18, 18') follow the same first cam track, at predetermined distance from each other so as to control the opening and the closing of the first half-mold and of the second half-mold in subsequent times during a same blowing cycle. - a first shaft (15, 15'), pivoting around an axis (D, B') thereof, parallel to the hinge axis, - a second shaft (16, 16'), pivoting around an axis (E, C') thereof, parallel to the hinge axis, - at least one first crank and at least one second crank integrally fixed to the first shaft, the at least one second crank having an end to which a first cam follower is fixed, and at least one third crank and at least one fourth crank integrally fixed to the second shaft, the at least one fourth crank (8, 8') having an end to which a second cam follower is fixed; or at least one first crank integrally fixed to the first shaft and a first cam follower hinged to said first shaft, and at least one second crank integrally fixed to the second shaft and a second cam follower hinged to said second shaft; - at least one first connecting rod (3, 3') hinged at a first end thereof to the first half-mold and constrained with a second end thereof to the first shaft (15, 15'), - at least a second connecting rod (4, 4') hinged at a first end thereof to the second half-mold and constrained with a second end thereof to the second shaft (16, 16'),