Yep - that's what running on the track at my healthclub did at 80% aerobic. Get a heart rate monitor and good running shoes.
When I started running, I would run 1 minute, walk 1 minute and then increased the split between run/walk to 2/1, 3/1, 4/1, 5/1 and am currently able to run 11/12 of a mile before needing to walk. Even the 1/1 split (the one minute walking should be an active recovery, so like the transitions in your program) helped and I noticed a difference as far back as last summer when I started on the easiest split.
Don't worry about not being able to get through your program immediately. You have to figure out where to actively breathe in programs in order to recover between elements.
Also, for spins, you need to breathe in on the entry and exhale during the revs, inhale on the change, etc. which will improve your strength in spins.