Which of these processes best to maintain the composition of the mantle? (1) the cyclic movement of the liquid in the mantle
(2) the cyclic movement between the mantle and the crust
(3) the interaction between the inner core and the mantle
(4) the interaction between the outer core and the mantle

The mantle is the layer between the crust and the outer core of the Earth. Only the mantle of the Earth is continually active.
The slow creeping motion of Earth's solid silicate mantle caused by convection currents carrying heat from the interior of the Earth to the surface is called mantle convection. So, the process that best helps to maintain the composition of the mantle is the interaction between the inner core and the mantle.

Do not include the unexpected results