I'm not wholly making this up; I just can't find the interview where I got this from (then again, it might be the interviews that were done in association with the 2006 remixes/remasters). But I recall Tony saying that this was a guy living in the aftermath of a nuclear disaster. The first verse is about that; there is the fire of destruction, and the creeping nuclear winter that he's running from ("pack on my back"). That's the part that gets me into this thread (haha!). I think the rest is subject to your interpretation, but I've always thought it was the fanciful memory of a past love (the "invent" is to signify that it's an idealized version of a past love; that rings true to me because so many of his songs have that evocative look at the past and it's something that resonates with me personally a lot). At the end he's walking "with her", that is, carrying her memory as he tries to make his way in this post-apocalyptic nightmare.