Rapid shape changes are observed for neutron-rich nuclei with A around 100. In particular, a sudden onset of ground-state deformation is observed in the Zr and Sr isotopic chains at N = 60: Low-lying states in N≤58 nuclei are nearly spherical, while those with N≥60 have a rotational character. Nuclear lifetimes as short as a few picoseconds can be measured using fast-timing techniques with LaBr3(Ce) scintillators, yielding a key ingredient in the systematic study of the shape evolution in this region. We used neutron-induced fission of 241Pu and 235U to study lifetimes of excited states in fission fragments in the A∼100 region with the EXILL-FATIMA array located at the PF1B cold neutron beam line at the Institut Laue-Langevin. In particular, we applied the generalized centroid difference method to deduce lifetimes of low-lying states for the nuclei 98Zr (N = 58), 100Zr, and 102Zr (N≥60). The results are discussed in the context of the presumed phase transition in the Zr chain by comparing the experimental transition strengths with the theoretical calculations using the interacting boson model and the Monte Carlo shell model.