A tool for facilitating operations for removing and fitting tires on wheels consists of a lever element provided, at one end, with a grip and maneuvering region and, at the opposite end, with an element for resting on the wheels and for acting as a fulcrum and with an element for mutually spacing the wheel rims and the tire beads that can be wedged between them. The apparatus includes a catcher ring component formed coextensive with the edge of one section of duct, and a catcher finger component formed coextensive with an edge of the other section of duct being coupled to form the joint. An intersecting point G immediately above the point P is determined, and a UV plane is defined on a tangent plane S2 with respect to the virtual sphere H.