Background: Neutron-rich nuclei around neutron number N = 60 show a dramatic shape transition from spherical ground states to prolate deformation in 98 Sr and heavier nuclei. Purpose: The purpose of this study is to investigate the single-particle structure approaching the shape transitional region. Method: The level structures of neutron-rich 93,94,95 Sr were studied via the 2 H( 94,95,96 Sr, t ) one-neutron stripping reactions at TRIUMF using a beam energy of 5.5 AMeV. γ -rays emitted from excited states and recoiling charged particles were detected by using the TIGRESS and SHARC arrays, respectively. States were identified by gating on the excitation energy and, if possible, the coincident γ radiation. Results: Triton angular distributions for the reactions populating states in ejectile nuclei 93,94,95 Sr were compared with distorted wave Born approximation calculations to assign and revise spin and parity quantum numbers and extract spectroscopic factors. The results were compared with shell-model calculations and the reverse (d, p) reactions and good agreement was obtained. Conclusions: The results for the 2 H( 94 Sr, t ) 93 Sr and 2 H( 95 Sr, t ) 94 Sr reactions are in good agreement with shellmodel calculations. A two-level mixing analysis for the 0 + states in 94 Sr suggest strong mixing of two shapes. For the 2 H( 96 Sr, t ) 95 Sr reaction the agreement with the shell-model is less good. The configuration of the ground state of 96 Sr is already more complex than predicted, and therefore indications for the shape transition can already be observed before N = 60.