Not quit sure what you are asking here. If you are asking how to blend the paint into the old paint, there is no way to do that. Just repainting the areas that are bubbling or peeling will cause flashing to happen, you will have to paint the hole wall or area again.

If you are talking about the seams of the mud, what you need to do is called feathering the seams into the existing drywall about 4 to 6 inches. If you go to my web site at http://www.stephensonpaint.com on our information page you will find pictures of a drywall repair I just did.

Then after you have done this the texture needs to be blended into the existing texture 6" to 12".

Start in the center o the area that was just repaired working your way out, as you get past the seams you just mudded the texture you are doing needs to get thinner thus blending it into the existing texture.
I hope this answer helps you, it is quite difficult to explain technique with out you having to read for hours.