  Obus-Wewers and Pop recently resolved a long-standing conjecture by Oort that
says: every cyclic cover of a curve in characteristic $p>0$ lifts to
characteristic zero. Sa\"idi further asks whether these covers are also
"liftable in towers". We prove that the answer for the equal-characteristic
version of this question is affirmative. Our proof employs the Hurwitz tree
technique and the tools developed by Obus-Wewers.
