Id start it off minor, a minor action resulting in a huge chain reaction, on both ends of the spectrum.
Lets just say, Reed Richards finds a loophole or something in a faulty teleportation machine, he exploits this; fixing it & also upgrading it without actually knowing.
He...lets say teleports an apple with a tracking device that he has put inside it. It instantly well dissapears, leaving Reed scratching his head for once.
Now, this apple has in fact been teleported to the DC universe...where? Anywhere I want it to be it could be DC Earth, Apokolips, Atlantis etc.
Now this apple will be completely ignore by most, but lets say oh, superman or someone comes across the apple and instantly recognises it isnt from the DC "Reality" because of some plot device power he has, and obviously see's a weird thingy inside it and thinks "boy, I should really get this interesting apple to someone really smart, maybe...Batman"
He takes the apple to Batman, who is pretty dumbfounded by where this apple comes from, but obviously realizes quite quickly that it has a tracking device inside it.
Unable to find its origin or locate the tracker, he puts it into storage until one day it is possible to do the former & the latter. Meanwhile in Marvel; Reed has given up on the apple and just carries on with his normal studies i.e save the world with something uber from time to time because I am that smart.
Now, back in DC, Brainiac 5 has came from the future to wage war, for whatever reason...
He obviously and easily finds Batmans batcave. He raids it personally with a few of his "bots" or whatever.
Comes across the apple, which he instantly realizes..."what the **** is that"
Now, Brainiac is defeated by JLA, but he has taken the Apple back with him to the 30th century(or 31st if you're picky) for furthur examination, breaks it all down with his superior intellect & superior and uber advanced tech that it is in fact, from a reality extremely similar to his own...he manages to reverse the tracking device so it is able to take him to its last location, but obviously for plot he sends it back in time to his younger self(the one living in the time he had previously waged war in) in the strongest theory he may be transported to a place that no longer exists, simply because of how far he is in the future from the time he actually swiped it from the Batcave.
Brainiac that is in the main time continuum recieves it, with instructions on what to do and what it is.
Now, upon transporting down the exact same path it travelled to get to DC...he has torn that very path inside out on itself, creating a portal for all to pass through(how? I dont know it just does for plot)
He is now in Reed Richards lab, who...well isnt home...braniac...being brainiac just takes allllllllllllll of reeds awesome universe busting capability thingy bobs back with him, and he quite clearly doesnt care about the portal, he just leaves it.
Reed arrives home, and reed being reed doesnt go thru the portal like an idiot, he monitors it blah nlah blah all nerd shit, and finds out that its a rip in reality, a literal doorway to another reality.
He alerts Sheild...and various other super groups and organisations.
So now A LOT of supers are involved, NY has been locked down.
A lot of abstracts and cosmic beings are also aware, BUT do not intervene unless they're threatened and they feel the Marvel U is threatened.
Of course Big G is on hand too, because of surfer, we see Galactus giving input etc etc etc (when really he only has his best interests at heart)
The Sentry, along with all other telepaths on earth mask New York from all outside interference ie no one can see whats happening.
But Loki being able to sense Thor's whearabouts and thoughts n shit, alerts all villains of this rip in reality. Along with various evil dudes having spies n shit infiltrating sheild and oter organisations at that current time so many villains know already, and alert the rest too.
OBVIOUSLY the exact same thing has been happening in DC.
Villains from both sides along with heros are all aware of this rip BUT have not passed through it yet.
From there I dont know where it would go or what would happen.
But what ever, Im not a writer. But it would just be a big uber series in which many die obviously and this time its not the cosmic forces or abstract entities forcing the battle, they are forced into battle themselves.