I think it's not the best of analogies.
DT's prog metal is more in the vein of what Fates Warning paved mixed with some early prog influences (Rush comes almost immediatly to my mind). of course unusual time signatures in rock are a trait in both in Tool and DT. But while DT are more into shredding/virtuoso and workshop like compositions where structures get lose into a myriad of solos and bridges just to converge again in a unissunous build, Tool are way tighter. Normally the structure remains way more static with a crapload of details and variations being added until finnaly the passage hits its zenith (a la Ravel's Bolero) and only then they move on.
As for Mastodon it's not that long of a stretch but the only blatant connection I see is Crack The Skye, where the guys (unfortunatelly IMO) changed a tad bit their sound from their first 3 albums (remain my favorites by far) to a lighter ssound and a more psychadelic /prog like structure. Those traits were kinda dropped in the following albums (with the exception of the more accessible sound)
Now Neurosis has that Ravel's Bolero like effect, but that's where simmilarities stops. While the majority of Tool's compositions always have at least a light at the end of the tunnel Neurosis is claustrophobic and neurotic (duh) as hell. There's no air to breathe and the ever growing repetitions instead of pulling you up are a spiral of adding layers to intoxicate you more and more. Besides that the time signatures are way more conventional. Neurosis adopted the Sludge genre created by bands such as Crowbar and EyeHateGod who had a Hard Core side into it (notice that the first two Neurosis albums are also hard core) and, in Souls At Zero, stripped it of that element, slowed down the tempo considerably and composed a sound even more oppressive, opening the doors of what many people call Post-Metal (don't like the label but it is what it is) and bands such as Cult Of Luna, Rosetta or Year Of No Light.
So here are the main bands/pivotal albums the band stated that influenced their sound. And if you mix it up together I think it's a fair portrait:
King Crimson (check Red)
Black Sabbath (but then again didn't these guys influenced everything that has heavy guitars?)
Faith No More (Blatant! That alterno-metal vibe... just check Angel Dust)
The Melvins (Although not being Sludge - way lighter - these guys paved the way to acts like Crowbar. If you want to trace a comparisson between The Melvins and Neurosis it's kinda like what the song Black Sabbath is to Cathedral's Forest Of Equilibrium in Doom Metal. Buzz is a massive influence to Adam).
Frederik Thornendal (time signatures and that stacatto touch Lateralus onwards)
Nine Inch Nails (Song crafting and ambiance)
Aphex Twin (Effects and shock factor)
And some state that the more psychadelic vein of early Pink Floyd also played a part (I can see a lot of interstellar Overdrive , Set The Controls To The Heart Of The Sun, Careful With That Axe Eugene, Astronomy Domine and Echoes among others on their compositions)