Anti-agathics are discovered in "At Death's End," which was incorporated, as the "New York" chapters, in They Shall Have Stars;
antigravity is derived from observations made in "Bridge," which was incorporated, as the "Jupiter V" chapters, in They Shall Have Stars;
the instantaneous Dirac transmitter is developed in "Beep," which was expanded as The Quincunx Of Time.
(Thus, so far, three stories have become two novels.)
They Shall Have Stars is the prequel to two volumes in which interstellar traders called "Okies" use anti-agathics, antigravity and the Dirac transmitter, then to one further volume in which the Okies' successors, the New Earthmen, use these technologies;
The Quincunx Of Time is linked to Midsummer Century by a peculiar application of the Dirac transmitter that was first revealed in "Beep" but is never discovered by Okies or New Earthmen.
Thus, despite the common reference to Dirac transmitters, these six volumes comprise two series. In fact, the kind of antigravity used in The Quincunx Of Time is that discovered not by the Bridge gang in They Shall Have Stars but by Adolph Haertel in Welcome To Mars. In the first case, flight to the Jovian system is necessary for the discovery of antigravity. In the second case, the discovery of antigravity initiates the first flight to Mars. In both cases, interplanetary travel is a prelude to faster than light interstellar travel.
When "Beep" was expanded as Quincunx, the new material included a Dirac message linking this work to the otherwise independent story, "A Style In Treason." Thus, the Dirac transmitter, having first appeared in what became the Cities In Flight (Okies) Tetralogy, span out of that series, in the process generating a second tetralogy:
Welcome To Mars
The Quincunx Of Time
"A Style In Treason"
Haertel, young in Welcome To Mars, is old in "Common Time," the opening story of a short trilogy in the collection, Galactic Cluster. And there are other connected but non-linear works that I have listed previously.
Blish was against my suggestion that a single long future history series might comprise the entire output of a science fiction writer's career. (This has never happened in practice.) First, during a writer's lifetime, scientific advances will invalidate the premises of his earlier stories. Secondly, any writer needs to be free to develop ideas in different directions which Blish clearly did, in the process generating several short cross-referring series.
As is legitimate in these circumstances, he commented on his main predecessor among future historians:
" 'Breeding for longevity in humans isn't practicable...' " (Cities In Flight, London, 1981, p. 74)