Before revision:  ~Theory predicts a shear flow induced migrationof colony of cells characterized by super-diffusive motion.
After revision:  ~Theory predicts a shear flow induced migrationof colony of cells characterized by super-diffusive motion of mesenchymal phenotype in the absence of flow. Interstitial flows regulate cell motility phenotype and promote the amoeboid over mesenchymal motility through adhesion interactions. Cells exhibit a dynamical slowing down of collective migration, with a decreasing degree of super-diffusion.