Divert- usually for "channeling" something, thus changing direction. Ex: divert attention, divert the water (of a river)
Shift- another change, usually temporary, a common process of change. Ex: shift gears in cars, shift weight from one foot to another, shift topics
Transfer-a deliberate change, almost the opposite of divert, can also be a transaction Ex:bank transfer, transfer attention from one person to another, football players transfer from team to team
Just my impressions