For the whole iOS 7 feel, I want to apply a blur effect to a specific portion of the screen to obfuscate it, but I don\'t want to just throw the blur on instantly, I want to
This is easy on OS X, where one view can CIFilter an effect onto the view behind it, and where the processor is powerful and fast. On iOS, however, there are no view-compositing filters, and blurring takes some time: you can't do it repeatedly, live, as fast as the animation's frames. Therefore some form of compromise is needed.
If you know far enough in advance what it is that you want to blur, however, you can prepare a series of images using a gradation of blurring: no blurring, a little blurring, a little more blurring, and so on. Then you assemble the images and "play" them as the "frames" of an animated UIImageView.
That, however, is not what I would actually advise. What I would do is prepare the blur image and the non-blurred image and use a CIDissolveTransition to dissolve from the non-blurred to the blurred image. No, it isn't the same as gradually applying the blur, but it is computationally inexpensive and is the best "dissolve" effect in the toolbox.