A delivery system for delivering a docking device to a native valve annulus of a patient's heart, comprising: an outer shaft; a sleeve shaft at least partially arranged within the outer shaft, the sleeve shaft comprising: a distal section configured to cover the docking device, the distal section comprising a flexible material with a lubricous outer surface; and a proximal section comprising a rigid material and including a tubular portion and a cut portion, the cut portion having an open, u-shaped cross-section; and a pusher shaft at least partially arranged within the outer shaft, the pusher shaft comprising: a main tube arranged interior to, in a radial direction that is relative to a central longitudinal axis of the delivery system, the sleeve shaft; an annular shell surrounding a proximal end portion of the main tube and spaced away from, in the radial direction, an outer surface of the main tube; and a proximal extension connected to and extending proximally from a proximal end of the main tube, proximal to the shell, the proximal extension comprising a flexible material and extending along a portion of an inner surface of the cut portion of the proximal section of the sleeve shaft. an outer shaft; a sleeve shaft at least partially arranged within the outer shaft, the sleeve shaft comprising: a distal section configured to cover the docking device, the distal section comprising a flexible material with a lubricous outer surface; and a proximal section comprising a rigid material and including a tubular portion and a cut portion, the cut portion having an open, u-shaped cross-section; and a pusher shaft at least partially arranged within the outer shaft, the pusher shaft comprising: a main tube arranged interior to, in a radial direction that is relative to a central longitudinal axis of the delivery system, the sleeve shaft; an annular shell surrounding a proximal end portion of the main tube and spaced away from, in the radial direction, an outer surface of the main tube; and a proximal extension connected to and extending proximally from a proximal end of the main tube, proximal to the shell, the proximal extension comprising a flexible material and extending along a portion of an inner surface of the cut portion of the proximal section of the sleeve shaft. a distal section configured to cover the docking device, the distal section comprising a flexible material with a lubricous outer surface; and a proximal section comprising a rigid material and including a tubular portion and a cut portion, the cut portion having an open, u-shaped cross-section; and a pusher shaft at least partially arranged within the outer shaft, the pusher shaft comprising: a main tube arranged interior to, in a radial direction that is relative to a central longitudinal axis of the delivery system, the sleeve shaft; an annular shell surrounding a proximal end portion of the main tube and spaced away from, in the radial direction, an outer surface of the main tube; and a proximal extension connected to and extending proximally from a proximal end of the main tube, proximal to the shell, the proximal extension comprising a flexible material and extending along a portion of an inner surface of the cut portion of the proximal section of the sleeve shaft. a main tube arranged interior to, in a radial direction that is relative to a central longitudinal axis of the delivery system, the sleeve shaft; an annular shell surrounding a proximal end portion of the main tube and spaced away from, in the radial direction, an outer surface of the main tube; and a proximal extension connected to and extending proximally from a proximal end of the main tube, proximal to the shell, the proximal extension comprising a flexible material and extending along a portion of an inner surface of the cut portion of the proximal section of the sleeve shaft.