Let G be a definable group, η= (E, p, X) a definable G fibration and f, h: Y → X definable G maps between definable G spaces. If f and h are definably G homotopic, then theinduced definable G fibrations f^* (η) and h^* (η) are definable G fiber homotopy equivalent.
Tomohiro KAWAKAMI (Fri,) studied this question.