We propose an analytical model to estimate the influence of a merger on the thermal SZ effect. Following observations we distinguish between subsonic and transonic mergers. Using analytical velocity fields and the Bernoulli equation we calculate the excess pressure around a moving subcluster for an incompressible subsonic gas. Positive excess around the stagnation point and negative excess on the side of the subcluster lead to characteristic signatures in the SZ map, of the order of $10\%$ compared to the unperturbed signal. For a transonic merger we calculate the change in the thermal spectral SZ function, resulting from bow shock accelerated electrons. The merger shock compression factor determines the power law tail of the new non-thermal electron population and is directly related to a shift in the crossover frequency. This shift is typically a few percent towards higher frequencies.