Complexes formed between cyclodextrins (CDs) and polymers-pseudopolyrotaxanes (PPRs) - are the starting point of a multitude of supramolecular structures, which are proposed for a wide range of biomedical and technological applications. In this work, we investigate the complexation of a range of cyclodextrins with Tetronic T1307, a four-arm block copolymer of poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) with a pH-responsive central ethylene diamine spacer, and its impact on micellization and the sol gel transition. At low concentrations, small-angle neutron scattering (SANS) combined with dynamic light scattering (DLS) measurements show the presence of spherical micelles with a highly hydrated shell and a dehydrated core. Increasing the temperature leads to more compact micelles and larger aggregation numbers, whereas acidic conditions induce a shrinking of the micelles, with fewer unimers per micelle and a more hydrated corona. At high concentrations, T1307 undergoes a sol gel transition, which is suppressed at pH below the pK(a,1) (4.6). SANS data analysis reveals that the gels result from a random packing of the micelles, which have an increasing aggregation number and increasingly dehydrated shell and hydrated core with the temperature. Native CDs (alpha, beta, gamma-CD) can complex T1307, resulting in the precipitation of a PPR. Instead, modified CDs compete with micellization to an extent that is critically dependent on the nature of the substitution. H-1 and ROESY NMR combined with SANS demonstrate that dimethylated beta-CD can thread onto the polymer, preferentially binding to the PO units, thus hindering self-aggregation by solubilizing the hydrophobic block. The various CDs are able to modulate the onset of gelation and the extent of the gel phase, and the effect correlates with the ability of the CDs to disrupt the micelles, with the exception of a sulfated sodium salt of beta-CD, which, while not affecting the CMT, is able to fully suppress the gel phase.