The local variations of group and phase propagation delays induced by bending and twisting a coupled core three-core fiber are experimentally characterized, for the first time, to the best of our knowledge, along the fiber length, with millimeter-scale spatial resolution. The measurements are performed by means of spectral correlation analysis on the fiber's Rayleigh backscattered signal, enabling for a distributed measurement of the perturbation effects along the fiber length. A mathematical model validating the experimental results is also reported.