The mechanism of propagation close to flame-flame interaction events is analysed using direct numerical simulation of a turbulent premixed methane-air flame. Four canonical local topologies arising from flame-flame interaction are identified in the vicinity of critical points. These correspond to reactant pocket, tunnel closure, tunnel formation and product pocket. The two spherical topologies (reactant and product pockets) are found to propagate consistently with no change in direction. Reactant pockets tend to propagate in the direction normal to the flame while product pockets tend to diffuse in the counter-normal direction. In contrast, both cylindrical topologies (tunnel closure and formation) may propagate either normally or counter-normally. It is shown that the direction of propagation for these topologies is strongly linked to principal curvatures of the flame surface. In such cases, the direction of propagation may reverse as the topology evolves and the principal curvatures change over time. Thus the conditioning on topology allows for more accurate estimation of displacement speed which is central to modelling turbulent flame speed.