We present population synthesis simulations of massive binary systems aimed at studying the impact of mass transfer on the formation of compact object binaries and gravitational wave progenitors. Using the SEVN code, we evolved three sets of $10^7$ binaries with metallicities representative of Population I, II and III stars, exploring different mass transfer efficiencies. We find that binaries undergoing at least one mass transfer episode are the main contributors to the population of binary black holes that merge within a Hubble time. Our preliminary analysis of semimajor axes of these systems shows a trend to be shorter, leading to shorter delay times. These results reinforce the importance of mass transfer in shaping the properties of compact object binaries and those of gravitational wave progenitors. Future work will extend this analysis to other compact objects types, metallicities and prescriptions for, e.g, angular momentum loss and common envelope ejection.