A machine for mounting and demounting a tyre relative to a corresponding rim of a vehicle wheel, comprising: - a column including a slideway extending along a vertical direction; - a wheel-holder unit rotating about an axis of rotation, parallel to the vertical direction; - a tool holder carriage that is movable along the slideway between a working position where it is close to the wheel-holder unit from above to operate on the wheel and a rest position, where it is away from the wheel-holder unit, wherein the tool holder carriage includes: a mounting tool, configured to be inserted between a bead of the tyre and an annular edge of the wheel rim in order to mount the tyre; a first arm; a demounting tool connected to the first arm and configured to be inserted between the bead of the tyre and the annular edge of the rim to demount the tyre, the first arm being movable slidably along a first horizontal sliding axis between a rest position, where it is retracted towards the column, and a working position, where it is extracted away from the column; a second arm; a bead seater tool, connected to the second arm and configured to operate on a sidewall of the tyre to apply a flattening pressure thereon; a third arm; a bead breaker disc connected to the third arm; characterized in that the second arm is slidably movable along a second horizontal sliding axis, spaced from the first horizontal sliding axis, between a rest position, where it is retracted towards the column, and a working position, where it is extracted away from the column. - a column including a slideway extending along a vertical direction; - a wheel-holder unit rotating about an axis of rotation, parallel to the vertical direction; - a tool holder carriage that is movable along the slideway between a working position where it is close to the wheel-holder unit from above to operate on the wheel and a rest position, where it is away from the wheel-holder unit, wherein the tool holder carriage includes: a mounting tool, configured to be inserted between a bead of the tyre and an annular edge of the wheel rim in order to mount the tyre; a first arm; a demounting tool connected to the first arm and configured to be inserted between the bead of the tyre and the annular edge of the rim to demount the tyre, the first arm being movable slidably along a first horizontal sliding axis between a rest position, where it is retracted towards the column, and a working position, where it is extracted away from the column; a second arm; a bead seater tool, connected to the second arm and configured to operate on a sidewall of the tyre to apply a flattening pressure thereon; a third arm; a bead breaker disc connected to the third arm; a mounting tool, configured to be inserted between a bead of the tyre and an annular edge of the wheel rim in order to mount the tyre; a first arm; a demounting tool connected to the first arm and configured to be inserted between the bead of the tyre and the annular edge of the rim to demount the tyre, the first arm being movable slidably along a first horizontal sliding axis between a rest position, where it is retracted towards the column, and a working position, where it is extracted away from the column; a second arm; a bead seater tool, connected to the second arm and configured to operate on a sidewall of the tyre to apply a flattening pressure thereon; a third arm; a bead breaker disc connected to the third arm;