(replace transit with transition as necessary, but it would probably not make any difference for you if you simply support both for now until existing data has been converted over time)

=== type=transit relations:

Is valid if there is exactly one "from" and one "to" member. Both must be ways, and they must touch end to end exactly once (so a transit relation where from and to way form a circle are invalid, if someone really has to map that, they will need to just split one of the two ways). You can warn about (if you want to) and otherwise ignore invalid relations. I will refer to this node as transit node" from now on.

--- Rules when splitting a way:

If the way to be split is the "from" or "to" member of a transit relation, then only the half of the way containing the transit node stays a member of the relation.

--- Rules when combining a way:

If the combined way is both the "from" and "to" member of a single transit relation, then delete the relation.

=== Transit tags on ways:

Only valid if the way does not form a closed loop.

Comes in different variants:

--- Only valid on one-way highways:

transit=*
transit:lanes=*

The transit node in this cases is the end node of the way where traffic flows out. (So depends on the direction of the way and the value [yes or -1] of the oneway tag).

--- Only valid on two-way highways:

transit:forward=*
transit:lanes:forward=*

The transit node in this cases is the end node of the way where traffic flows out in "backward" direction. (So depends on the direction of the way. [I don't think left or right hand traffic is important?]).

transit:backward=*
transit:lanes:backward=*

The transit node in this cases is the end node of the way where traffic flows out in "forward" direction. (So depends on the direction of the way. [I don't think left or right hand traffic is important?]).

A way may have both forward and backward tags, the transit node for each one is different in that case!

--- Rules when splitting a way:

The transit tag stays with the half that contains the transit node.

--- Rules when combining a way:

No special handling.