A thrust compensation kit for a sash of a lift-and-slide window or door, comprising: - a fixing bracket that is stably applicable in a receiving seat obtained on a lower cross member of the sash so as to be movable solidly to said sash between a raised position and a lowered position, said fixing bracket comprising an abutment projection; - a containment body insertable into the receiving seat and hollow so as to house, in use, a connection bar between movement carriages (300a, 300b) for moving said sash in a configuration in which the connection bar is parallel to a prevalent direction of extension of the containment body, said containment body having a first end configured to abut on said abutment projection and a second end, opposite the first end and having an access opening; - an elastic contrasting means extending in the containment body starting from said first end and fittable, in use, around the connection bar, said elastic contrasting means being compressible or extendible along the prevalent direction of extension of the containment body; - a thrust body at least partially housed slidingly inside said containment body and having a first end facing said elastic contrasting means and a second end, opposite the first end and configured to generate a thrust on one of said movement carriages (300a, 300b) for moving the sash, said thrust body being slidable through said access opening between a retracted position, in which said elastic contrasting means is compressed, and an extracted position, in which said elastic contrasting means is at least partially extended, said thrust body being hollow to enable, in use, a housing of the connection bar. - a fixing bracket that is stably applicable in a receiving seat obtained on a lower cross member of the sash so as to be movable solidly to said sash between a raised position and a lowered position, said fixing bracket comprising an abutment projection; - a containment body insertable into the receiving seat and hollow so as to house, in use, a connection bar between movement carriages (300a, 300b) for moving said sash in a configuration in which the connection bar is parallel to a prevalent direction of extension of the containment body, said containment body having a first end configured to abut on said abutment projection and a second end, opposite the first end and having an access opening; - an elastic contrasting means extending in the containment body starting from said first end and fittable, in use, around the connection bar, said elastic contrasting means being compressible or extendible along the prevalent direction of extension of the containment body; - a thrust body at least partially housed slidingly inside said containment body and having a first end facing said elastic contrasting means and a second end, opposite the first end and configured to generate a thrust on one of said movement carriages (300a, 300b) for moving the sash, said thrust body being slidable through said access opening between a retracted position, in which said elastic contrasting means is compressed, and an extracted position, in which said elastic contrasting means is at least partially extended, said thrust body being hollow to enable, in use, a housing of the connection bar.