  The main purpose of this paper is to investigate the concept of maximal
$L^p$-regularity for perturbed evolution equations in Banach spaces. We mainly
consider three classes of perturbations: Miyadera-Voigt perturbations,
Desch-Schappacher perturbations, and more general Staffans-Weiss perturbations.
We introduce conditions for which the maximal $L^p$-regularity can be preserved
under these kind of perturbations. We give examples for a boundary perturbed
heat equation in $L^r$-spaces and a perturbed boundary integro-differential
equation. We mention that our results mainly extend those in the works: [P. C.
Kunstmann and L. Weis, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 30 (2001),
415-435] and [B.H. Haak, M. Haase, P.C. Kunstmann, Adv. Differential Equations
11 (2006), no. 2, 201-240].
