Inital CBEQo sometimes represent the CarryBorrow flag or it's inverse.
Othertimes, represents EQ, a magnitude comparator control line.

Something else I had drawn. Nothing new here but maybe clarifies Manchester chain.
Any of these chains can easily do the job of another, but Carry is actually the oddball.
CBEQ and Worrob all positive logic true by when wired for subtraction by default.
2's comp and inverse flag allowed, but not required. Works fine either way.

In each twin MUX lives an internal 4way decoder to drive transmission gates.
Those hidden internal gate drives might be the actual arithmetic prefixes.
External prefix control lines only modify non-propagate replacement rules.
In relays, there are no gate drives. Mechanical position acts as the prefix.
A vs B is enough to set all switches in parallel time without waiting on C.

We solve the prefixes at wire speed by passing series current through.
Rather than solve in parallel by the usual tree of combinatorial logic.
A string of RC propagation and capacitive fanout delay per slice vs a tree
several combinatorial gate delays deep. What circumstance favors each?

I dunno if you've read Ken Shirriff's reverse engineer of the i8086 ALU.
Totally different Ken, not my blog. But we discover an ALU that operates
by many of the same principals. Carry chain a little different, not much.
Series not just for folks that can't make sense of a parallel prefix tree.

Just don't take the idea too far and try to stack an absurdly short chain.
Once was enough to swear never again...