Several cards from the elemental cycle, specifically Asako Azunami (The Ebb and Flow 066), All and Nothing (All and Nothing 095) and Restored Heirloom (Elements Unbound 117) have interrupt abilities that trigger when the effect of a particular ring would resolve. Contrast interrupts that trigger when the effects of events would initiate. The Initiating Abilities/Playing Cards entry of the rules reference makes it clear that events initiate at step 6 but don't resolve until step 7 but there is no equivalent distinction for ring effects in step 3.2.6 of conflict resolution when rings are resolved. Do ring effects initiate before they resolve like action abilities? I ask because I'm unsure how the timing of these cards interacts with Pilgrimage (Core Set 022). Does Pilgrimage cancel ring effects before they can be replaced or can these interrupts replace ring effects before they are canceled?

Just now, Bayushi Shunsuke said:

Several cards from the elemental cycle, specifically Asako Azunami (The Ebb and Flow 066), All and Nothing (All and Nothing 095) and Restored Heirloom (Elements Unbound 117) have interrupt abilities that trigger when the effect of a particular ring would resolve. Contrast interrupts that trigger when the effects of events would initiate. The Initiating Abilities/Playing Cards entry of the rules reference makes it clear that events initiate at step 6 but don't resolve until step 7 but there is no equivalent distinction for ring effects in step 3.2.6 of conflict resolution when rings are resolved. Do ring effects initiate before they resolve like action abilities? I ask because I'm unsure how the timing of these cards interacts with Pilgrimage (Core Set 022). Does Pilgrimage cancel ring effects before they can be replaced or can these interrupts replace ring effects before they are canceled?

Pilgrimage cancels ring effects before they can be interrupted by the cards you listed.

[Tyler Parrott, Jan 9 2019]