Action Comics reached #1000, DC handed the keys to the Superman kingdom to Brian Michael Bendis, and reset Superman to #1 yet again. Along with the “Superman Rebirth” map with the Tomasi and Jurgens runs, these volumes are designed to work around the main DC Rebirth narrative, although it turns out that the entire run takes place between “Doomsday Clock” and “Flash Forward” from that map. Also, as usual when Bendis is writing two titles of the same franchise, the chronology doesn’t always match up nicely between the two series. Hence some splicing of issues and arcs in this map. Any Superman issues refer to volume 5 of the series:
-Volume 1 was the original Superman series that began in 1939, renamed to Adventures of Superman in 1987, reverted to Superman in 2006, and was ended at #714.
-Volume 2 was the post-Crisis series that ran for 226 issues between 1987 and 2006.
-Volume 3 was the New 52 series launched in 2011. (#715-766)
-Volume 4 was the Rebirth series launched in 2016. (#767-811)
-Volume 5 is the series relaunched by Bendis in 2018.
Action #1000 (last story)
DC Nation #0 (middle story)
Man of Steel #1-6
Superman #1-6 (except last two pages of #6) [812-817]
Ideally, I would have liked to have put all of Superman #1-15 together, and then put Action #1001-1011 with the Leviathan special. But the biggest kink in the continuity flow is the return of a character on the last two pages of Superman #6 which leads directly into #7. Action Comics #1001 could possibly go before Superman #1, based on a character referring to a scene from Man of Steel #2 as yesterday. However, I have come to the conclusion that Bendis considers anything that happened before today as “yesterday”.
Leviathan Rising #1
Superman #6 (last two pages)
Superman #7-15 [818-826]
Supergirl #31-32 were advertised as a crossover with Superman #12-13, yet neither set of issues references the other. Plus, both series were released on the same day, so publication order does not even help. Both series just show their title character’s perspective on the events going on. The Supergirl segment of Leviathan Rising says it takes place after Supergirl #32, and three months after Action #1009, so that part can only be explained as a flashforward.
Year of the Villain #1 (middle story)
Event Leviathan #1-6
Superman #16 
There’s really no good way to organize all of the plotlines going on in Superman, Action, and Event Leviathan. Action #1012 opens with a scene that looks like it should take place in the middle of Superman #10 before he heads off to space. At the beginning of Event Leviathan #1, Lois mentions Superman away on family business, which is a reference to Superman #7-15. There’s another reference in Superman #10 before he goes into space where Lois says that she’ll handle Leviathan. My handwave solution is to say that Superman goes off on his space adventure in Superman #10-15, returns for his adventures in Action #1012-1016, then off-panel, gets called back out to space for some aftermath which is why he’s absent from the first three issues of Event Leviathan.
Also, DC started the “Year of the Villain” event which tied into Scott Snyder’s Justice League run and ultimately led into Dark Knights: Death Metal. I have opted to skip all of that except for Death Metal.
Superman #17 
Superman #18 
Leviathan Dawn #1
Superman: Heroes #1
Superman: Villains #1
There are copious amounts of continuity notes within the issues, but it’s not clear if all of them are accurate. Most of them deal with a major event that occurs in Superman #18. That event is referenced as “tomorrow” in Action #1017-1021, as as “this morning” in Leviathan Dawn #1. There is a break halfway through Superman #19 that leads into Superman: Heroes, but splicing would require scan-and-print. I prefer to include it as a “prologue” in the next volume.
The House of Kent
Superman #19-28 [830-839]
Action Comics #1022-1028
There is a major continuity confusion with the arc in Superman #19-22 and the Villains one-shot, specifically the fight with Mongul. In Superman: Villains, we see Mongul the son kill Mongul the father and then go off to fight Superman. It’s heavily alluded that this leads into Superman #19. But at the end of Superman #22, there’s an editor note directing the reader to Superman: Villains for the fate of Mongul. It’s never clear if the Mongul in the Superman arc is the son or the father in the Villains special. I choose to go with the sequence of events that the son kills the father and then goes to fight Superman, hence this mapping.
Greg Rucka wrote a Lois Lane series and Matt Fraction wrote a Jimmy Olsen series around this time, but they are almost impossible to mesh with the Bendis run. It’s best to leave those off to the side, with the possible exception of Lois Lane #6 as an epilogue to Event Leviathan. There are some nice concepts and theories that get introduced in the final issues of Lois Lane that go along with the meta-reboot of the DCU, but ultimately the narrative just doesn’t fit.
Bendis also planned a second Leviathan mini-series that was later cancelled/postponed. If it even gets published, there’s no telling if it will take place during this time frame or not.