Rush's road manager Howard Ungerleider came up with the title at a party. There were two dogs at the party, one a German shepherd and the other a tiny white nervous dog. Howard used to call the shepherd By-Tor because anyone that walked into the house was bitten. The other dog was a snow-dog (white). So from that night on Howard called the pair of dogs "By-Tor and the Snow Dog." The dogs belonged to Rush's manager.
The song is divided into 4 chapters: I) At the Tobes of Hades, II) Across the Styx, III) Of the Battle, IV) Epilogue. Chapter 3 (Of the Battle) is divided into 4 chapters in and of itself: i) Challenge and Defiance, ii) 7/4 War Furor, iii) Aftermath, iv) Hymn of Triumph. Total running time, according to the label, is only 8:37.
On the back cover of the album Alex Lifeson is identified as "Snow Dog", and Geddy Lee is identified as "By-Tor".
The character By-Tor returned on the following release, "Caress of Steel." In that song, By-Tor was the victor in the battle. (thanks, Jeff - Haltom City, TX, for all above)
This was the first Rush album with Neil Peart, their drummer and lyricist who became an integral part of the group.
There is a video created for the Vapor Trails tour that played on screen behind stage. This is also a hidden feature on the Rush In Rio DVD (Easter egg) accessible on the second disc (Boys in Brazil). (thanks, Mike - Mountlake Terrace, Washington)
Section III was originally called "The Battle."
On the original vinyl album, the chimes at the end were printed into the fadeout groove of side one. On older turntables, until the stylus was physically lifted from the vinyl, the chimes would keep playing. On the Archives version, the song is 28 seconds longer as additional chimes were included. (thanks, Mike - Mountlake Terrace, Washington, for above 2)