Apparatus for controlling start-up and shut-down of a pump of a water distribution network, comprising: - a chamber provided with an inlet which can be operatively associated with the delivery side of a pump and an outlet operatively connected to the water network, - a system for detecting and/or measuring the flow of water through said outlet adapted to emit a start-up signal for the pump upon reaching a preset flow threshold value, - a device for detecting and/or measuring the pressure in said chamber adapted to emit a start-up signal for the pump of the network upon reaching a preset value defined "cut-in pressure", - electronic controlling and managing means for controlling and managing operation of the device, - a plurality of preset cut-in pressure values stored in said electronic control and management means, and interface means available to the user to select one of the preset cut-in pressure values of said plurality of preset cut-in pressure values, characterized in that said device for detecting and/or measuring the pressure in said chamber comprises: - sensor means, sensitive to the magnetic field, adapted to produce an effect/signal when the size of the magnetic field that surrounds said sensor means exceeds a given operating value, said effect/signal being correlated with the drive of said pump, - a body sensitive to the pressure in said chamber, movable along a direction as a function of the pressure value in said chamber in such a manner that a portion thereof moves toward or away from said sensor means on the basis of the pressure in said chamber, - magnetic means integral with said portion of the movable body, adapted to produce a magnetic field, defined primary magnetic field, the value of the primary magnetic field that surrounds said sensor means being correlated to the pressure value in said chamber, the position of said body, or the distance of said magnetic means from said sensor means, being a function of the pressure in said chamber. - a chamber provided with an inlet which can be operatively associated with the delivery side of a pump and an outlet operatively connected to the water network, - a system for detecting and/or measuring the flow of water through said outlet adapted to emit a start-up signal for the pump upon reaching a preset flow threshold value, - a device for detecting and/or measuring the pressure in said chamber adapted to emit a start-up signal for the pump of the network upon reaching a preset value defined "cut-in pressure", - electronic controlling and managing means for controlling and managing operation of the device, - sensor means, sensitive to the magnetic field, adapted to produce an effect/signal when the size of the magnetic field that surrounds said sensor means exceeds a given operating value, said effect/signal being correlated with the drive of said pump, - a body sensitive to the pressure in said chamber, movable along a direction as a function of the pressure value in said chamber in such a manner that a portion thereof moves toward or away from said sensor means on the basis of the pressure in said chamber, - magnetic means integral with said portion of the movable body, adapted to produce a magnetic field, defined primary magnetic field, the value of the primary magnetic field that surrounds said sensor means being correlated to the pressure value in said chamber, the position of said body, or the distance of said magnetic means from said sensor means, being a function of the pressure in said chamber.