A conveyor for transporting pieces in a production line, comprising: - a carousel rotatable about a vertical axis of rotation and defining a closed feed path for said pieces; - a station for feeding raw parts to a processing machine set up along said closed feed path; - a station for collecting pieces processed by said processing machine set up along the closed feed path; - a plurality of units angularly distributed on said carousel and configured for each receiving a stack of raw pieces or a stack of processed pieces, preferably said pieces being circular or parallelepiped-shaped, characterized in that each of said units extending along an axis of extension inclined away from and/or towards said axis of rotation and comprising: - a base plate configured to support the bottom of a stack of pieces, said base plate being movable along said axis of extension between a position distal from said carousel, in such a way as to release said raw pieces in said feed station, and a proximal position relative to said carousel for receiving said pieces processed in said collecting station, preferably said base plate being movable up and down by an amount equal to a thickness of the pieces forming the stack; - a pair of supporting elements extending along said axis of extension to define a movement guide for said base plate, said supporting elements delimiting with the respective base plate a seat for containing a piece or a stack and acting in conjunction with said base plate to perform a self-centring of the piece or stack of pieces. - a carousel rotatable about a vertical axis of rotation and defining a closed feed path for said pieces; - a station for feeding raw parts to a processing machine set up along said closed feed path; - a station for collecting pieces processed by said processing machine set up along the closed feed path; - a plurality of units angularly distributed on said carousel and configured for each receiving a stack of raw pieces or a stack of processed pieces, preferably said pieces being circular or parallelepiped-shaped, characterized in that each of said units extending along an axis of extension inclined away from and/or towards said axis of rotation and comprising: - a base plate configured to support the bottom of a stack of pieces, said base plate being movable along said axis of extension between a position distal from said carousel, in such a way as to release said raw pieces in said feed station, and a proximal position relative to said carousel for receiving said pieces processed in said collecting station, preferably said base plate being movable up and down by an amount equal to a thickness of the pieces forming the stack; - a pair of supporting elements extending along said axis of extension to define a movement guide for said base plate, said supporting elements delimiting with the respective base plate a seat for containing a piece or a stack and acting in conjunction with said base plate to perform a self-centring of the piece or stack of pieces. - a base plate configured to support the bottom of a stack of pieces, said base plate being movable along said axis of extension between a position distal from said carousel, in such a way as to release said raw pieces in said feed station, and a proximal position relative to said carousel for receiving said pieces processed in said collecting station, preferably said base plate being movable up and down by an amount equal to a thickness of the pieces forming the stack; - a pair of supporting elements extending along said axis of extension to define a movement guide for said base plate, said supporting elements delimiting with the respective base plate a seat for containing a piece or a stack and acting in conjunction with said base plate to perform a self-centring of the piece or stack of pieces.