To transfer the stitches from a first needle arc (7X) to a second opposed needle arc (7Y), a overturnable semicircular sector (19) presents elements (25) terminating in a bifurcate way (25F) (flanking inside the respective sinkers (11) the relevant needle (7X) of the first arc), each of which has an upper fork projection (25A) embracing the needle (7X) and forming a rear recess (25X) and a front recess (25C) suitable to engage an end stitch (M1) formed by the corresponding needle (7X), said stitch (M1) then being transferred and engaged on a corresponding needle (7Y) of the second needle arc.