How are different Animation Controllers sequenced?

How can multiple Animation Controllers be linked to each other then called to play in a sequence? I'm using C# but am opened to how this can be done in the State Machine as well.

For instance, three different cards each have unique controllers attached since they each have different behaviors. One slides in from the top, the others appear from left and right, tumbling and scaling respectively.

I already have a button that can call/play each card from a list and it works fine. Using a reverse button it plays backwards ... perfect

However what I'd like to do is 'autoplay' this list. So from whatever card is current, hit this button that accesses this same list of cards and plays them in sequence automatically.