A cutting equipment which trims strips of webs in movement includes a stationary trimming blade and a rotating cylinder with a mobile trimming blade; the rotating cylinder includes a sector with suction openings connected to a vacuum source, which retains the strips by suction and drags the strips up to a strip collector; the cutting equipment cuts and separates transversal strips of two webs overlapped in adherence jointly to the cutting of basic sheets; a perforating device perforates a row of holes on the first web adjacent to an edge of the sheets; and a first web is positioned with the row of holes in front of the suction openings, while the strip of the second web is retained and dragged by suction through the holes of the first web up to the strip collector.