In can-annular gas turbines, low-frequency thermoacoustic instabilities can arise from cross-talk interactions between neighboring combustors upstream of the first-stage turbine nozzles. In this experimental study, we investigate the influence of non-identical flame transfer functions (FTFs) between adjacent combustors on the development of self-excited thermoacoustic oscillations. To create different FTFs, we use five different swirl nozzles, one with high swirl (HS) and four with low swirl (LS), all with different porosities. We find that, compared with the LS FTFs, the HS FTF exhibits a smaller and flatter gain as well as a smaller phase difference. We attribute this behavior to differences in the flame structure and the stabilization mechanisms, namely an inner shear layer-stabilized diverging front in the HS case versus a detached reaction zone in the presence of a central jet with an outer swirl flow in the LS cases. Using two tunable lean-premixed combustors connected via a cross-talk section, we show that (i) symmetric FTF combinations (HS + HS or LS + LS) produce in-phase interactions, leading to push-push modes, but that (ii) asymmetric FTF combinations (HS + LS) produce out-of-phase interactions, leading to push-pull modes. Phase-resolved visualization of the asymmetric cases reveals that the inner shear layer-stabilized HS flame exhibits large angle fluctuations, whereas the aerodynamically stabilized LS flame is characterized by the periodic emergence of a bow-shaped front and an oval structure. For all the conditions tested, we find that asymmetry in the FTFs leads to either (i) a completely stable state with negligible amplitude or (ii) a mildly unstable state with an amplitude lower than that of the equivalent symmetric cases. These findings highlight the potential of using asymmetric FTFs for passive control of cross-talk-driven thermoacoustic instabilities in can-annular combustors.