I've always wondered why the M3W doesn't have a crossover like almost all V2 engines. So I had one custom-made. Visually, I think it turned out really well, and the results are phenomenal: better torque in the low and mid-range RPMs, smoother engine operation, a fuller, more refined sound, and lower fuel consumption. Some pics:
Both manifolds are stock. The pipes and tailpipes had been upgraded to Stage 3 by the previous owner and were completely open along their entire length (massively oversized). They were very loud, with a whip-like noise on the overrun—very unpleasant. With the crossover this negative effect is almost gone. Crossover makes sense for both stock and straight-through pipe system. This crossover can be easily removed for engine maintenance. Crossover diameter is 38 mm.
In essence the exhaust pulses of one cylinder aid scavenging of the other. Moto Guzzi V twins had a crossover on the front pipes or via an H section under engine or both.