How can I chain Core Animations for different Layers one after the other?

The beginTime property of a CAAnimation only seems to work if the CAAnimation is part of a CAAnimationGroup. I think you'll also need to set the duration property of the CAAnimationGroup large enough to last until its final animation completes.

https://stackoverflow.com/a/563486/77567

Actually, it turns out that the key is getting the current time in terms of a frame of reference and adding any time offset to that current time. This works also for non-grouped animations.

For instance, something along the lines of this code would cause n layers (assumed to be stored in some array) to sequentially fade in one after the other, each taking .8 secs.:

CGFloat timeOffset = 0;

[CATransaction begin];

for (CALayer *layer in layers) {
    CABasicAnimation *a = [CABasicAnimation animationWithKeyPath:@"opacity"];

    a.fromValue = @(0);
    a.toValue = @(1);
    a.fillMode = kCAFillModeForwards;
    a.beginTime = [layer convertTime:CACurrentMediaTime() fromLayer:nil] + timeOffset;
    a.duration = 0.8;
    a.removedOnCompletion = NO;

    [layer addAnimation:a forKey:nil];

    timeOffset += a.duration;
}

[CATransaction commit];

In the above case, the frame of reference is simply the current time when the invocations take place.