Hi Stephen.
Just went through that myself. My son and I did our pair of 06 BAs. The air box is a tricky thing, and seems to want to wiggle out only one way. It worked best for us to pull the pipes, and then jack the stand up until the swing arm is just shy from touching the rectifier(?) on the back of the frame under the swing arm.
The back end of the box needs to drop down, and then out at a downward angle. Watch the two tabs on the right side - one of the left top cover screws will want to push it to the side and break them off. When it's mostly out it can then be turned counter clockwise a quarter turn, and then slid out along between the tire and fender out the back. The bottom of the box will follow the profile of the tire.
I had the air box in and out quite a few times to think and measure the cuts I wanted. The first time you do it it'll be a two or three beer job, after that it's in and out between swigs!!
We didn't have to take the fuse box off the battery tray. Just the two bolts at the bottom of the tray, and the one lower down that goes into the side of the frame. The whole affair can then be moved to the side enough to slinky the box out.
Hope this helps
