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The LIGO-Virgo-KAGRA (LVK) Collaboration has reported nearly 100 BH-BH mergers. The LVK provides estimates of rates, masses, effective spins, and redshifts for these mergers. Yet, the formation channel(s) of the mergers remains uncertain. One way to search for a formation site is to contrast properties of detected BH-BH mergers with different models of BH-BH merger formation. Our study is designed to investigate the usefulness of the total BH-BH merger mass and its evolution with redshift in establishing the origin of gravitational-wave sources. We find that the average intrinsic BH-BH total merger mass shows exceptionally different behavior for the models that we adopt for our analysis. In the local universe (z=0) the average merger mass changes from Mtot,int=25Msun for CE binary evolution and open clusters formation channels, to Mtot,int=30Msun for the stable-RLOF binary channel, to Mtot,int=45Msun for the globular cluster channel. These differences are even more pronounced at larger redshifts. However, these differences are diminished when considering LVK O3 detector sensitivity. Comparison with LVK O3 data shows that none of our adopted models can match the data despite large errors on BH-BH masses and redshifts. We emphasize that our conclusions are derived from a small set of 6 models that are subject to numerous known uncertainties. We also note that BH-BH mergers may originate from a mix of several channels and that other (than those adopted here) BH-BH formation channels may exist.