They merge into a single organization, with a single hierarchy, while endorses the confessional/doctrinal statements of both traditions, while maintaining congregations that are continuous with either one or the other tradition, or are combined congregations. The liturgy is then made adaptable to either tradition. If you're interested, look at what the Church of South India did in the mid-20th cent., how it merged, how they handled the liturgical/worship differences between the various constituent groups, etc. I suspect that if the mainline U.S. churches continue to shrink, there'll be talk about some sort of merger like that between them. The resulting body would still be the American representative in the Anglican Communion, and the official liturgy would probably be something very similar to the 1979 BCP, with elements drawn from other traditions, but there would be individual congregations within it that aren't Anglican.