The left hand rise was Greenspan handing off to BB. They then had the space to lower rates into when the engineered drop was started, in earnestin late 2007. All the signs were there even as early as late 2006 that it was not in good health.
rates started going up in 2004 to facilitate this:
https://www.thisismoney.co.uk/money/news/article-1506638/Greenspan-raises-US-rates.html