Nas said why he wasn't phuckin' wit Jay-Z back in the day. It was because he was a Bklyn dude. The only reason why he was cool with AZ was because he was already runnung with AZ, and he used to hang in Queensbridge wit' him and they would battle dudes around the city.
Take it back...Mid 90's and Nas wanted to be the K.O.N.Y. He was praised as the 2nd coming of Rakim, the greatest rapper to speak in a long time, the dude that was gonna show niggas how to rhyme, and be vivid with ghetto stories. Wu-Tang had already dropped and was re-ing up on the solo releases, Biggie really came outta nowhere (his debut album was nowhere near as anticipated as Illmatic) and blew up, and because of record sales/exposure, people were sayin' this Bklyn dude is now K.O.N.Y. Nas/Wu/Mobb form a lil alliance (see Shark Niggaz/Verbal Intercourse/Eye For An Eye/Right Back At You), and Biggie forms an alliance wit' Jay-Z. Nas dropped It Was Written and sent a subbie shot at Biggie with the line..."So let me let y'all niggas know one thing/There's one life one love so there can only be one king"
After IWW dropped it was announced that Nas/AZ/Foxy/Mega would make up The Firm. Biggie, not to be outdone, decided to make The Commission with Biggie/Jay-Z/Charlie Baltimore/Cam'Ron. Jay drops Reasonable Doubt and reaches out to Nas but Nas is not trying to help other rappers outside of his alliances, and especially a Bk dude who is gettin' down wit' Biggie. Biggie records Life After Death and throws subbies on "Kick In The Door" at Raekwon/Ghostface
(This goes out for those that choose to use
Disrespectful views on the King of NY
F*ck that, why try, throw bleach in your eye
Now ya Braille in it, stash that light sh*t, or scalin it)
& Nas
(Ain't no other kings in this rap thing
They siblings, nothing but my chil'ren
One shot, they disappearin'
Its ill when, MC's used to be on cruddy sh*t
Took home, Ready to Die, listened, studied sh*t
Now they on some money sh*t, successful out the blue
They light weight, fragilly, my nine milly
make the white shake, thats why my money never funny
And you still recoupin, stupid)
As far as the "showed you ya first tec on tour wit' Large Professor" line, the story is Jay-Z was on tour wit' Jaz, and Nas was on tour wit Xtra P and they were backstage and Nas had some beef/trouble with somebody and Jay-Z had his back and let him hold the Tec-9 to hold himself down.
There was never nothing serious (at least not yet) between Nas & Biggie, just a few competitive subbies.