references included in this response. GST (as R3 remarked) and that (ii) the Diffusion GST is very similar to the method in [W1] which has been compared

We thank all the reviewers and the AC for their time, effort and constructive feedback. First, we will include an explicit comparison with the GST of [W1]. This is required to control the impact that topology changes have on the eigenvectors. Likewise, since Prop. 2 shows stability of the graph The formal assumption in Prop. 3 indicates that all involved graph filters in the multirresolution wavelet bank have to The hypothesis in Prop. 3 will be changed to reflect this. Theorem 1 states that it does not depend on the spectral norm of the graph.