I think they have a bit of all three while still sounding unique. The Tool-influence to me can be found in their more rhythmical stuff, because Tool's music is a lot about rhythm and almost hypnotizing/mesmerizing chord progressions. I think it's more noticeable in some of their longer songs like "
Dance With the Shadow", which has a few parts like that. (The "Join in the shadow dance"-part for example)
Regarding the PT-influence I think it's easy to hear both eras of PT in Riverside. "
Volte-Face" has an intro which reminds me quite a lot of Signify, and the first time I heard the song, that was the first thing to pop up in my mind. I think the first three albums in particular has a certain progressive sound that isn't miles away from what PT did on Signify for example. But on the other hand you have a song like "
Conceiving You" which sounds like it could be very influenced from SW's newer ballad-songs, something from IA or Deadwing for example. Speaking of songs that sounds similiar to PT, "
Driven to Desctruction" and So Called Friend anyone?
It's a bit tricker with the Anathema-influence, because I don't think that one is something you hear as much as the music reminds you of Anathema, and their way of making progressive music. A melody here or there, the dark and almost depressive atmosphere you can find on the earlier Riverside-albums.
But yeah, I'd also say a bit of Dream Theater-ness as well. Riverside aren't as flashy or technical, but they can craft long songs like few bands can. There's pretty much long epics on all albums, songs like "
Ultimate Trip" (13 mins), "
Second Life Syndrome" (15 mins), "
The Same River" (12 mins), "
Left Out" (11 mins), "
Hybrid Times" (12 mins) and "
Forgotten Land" (10 mins) are all pretty much among the best songs the band has made. Add to that "
Escalator Shrine" (13 mins) from the new album which is awesome.
So yeah, you're in for a treat.