The USS Equinox is briefly visible on the screen when Seven of Nine shows Janeway the Cardassian ship in Astrometrics among the fifty-two ships that Neelix's ship's sensors recorded at the Caretaker's array in The Voyager Conspiracy (1999).
The episode establishes that the Voyager is now about 35,000 light years away from the Alpha Quadrant.
The USS Equinox is a Nova-class starship. According to the Star Trek: The Next Generation (1987) Technical Manual," the Nova-class starship was originally considered as a successor to the Galaxy-class starship, and as a possible design for the Enterprise-E which first appeared in Star Trek: First Contact (1996).
The main bridge of the Equinox is a re-use of the set used for the USS Prometheus, as are the corridors, crew quarters and science lab. They are all slightly altered to simulate the effect of damage.
In Relativity (1999), we see Admiral Patterson introducing Janeway to The Doctor for the first time, remarking that Starfleet was considering outfitting his program onto all Federation star-ships. The Equinox apparently was another test candidate for the Lewis Zimmerman EMH program, as it must have been in the Delta Quadrant at that time or shortly after.