The theory of frames is nowadays play an important roles in the studying of Hilbert and Banach spaces. Also the notion of redundancy is a new concept that shows essential properties of a frame. In this paper, after a short review on frames and fusion frames, we present an approach for the studies in the area of frame theory based on the notion of redundancy. An interesting question about the perturbed sequences is: when do they inherit the properties of the original one. An elegant relation between a frame (fusion frames) and their perturbations is the relation of their redundancies. In this paper, we investigate these relationships.
