This is true for triggered effects like "
Sangan" or "
Night Assailant" when it's discarded to the Graveyard. Continuous effects can and will be able to interrupt the chain resolution. It would also appear that 'some' triggered effects that involve
Card Destruction will also be able to interrupt chain resolution as well. This would include effects like "
Spirit Reaper"s self destruct and "
Gearfried the Iron Knight"s Equip Destruct effects.
Unfortunately, that's not the case here. "
Spirit Reaper" will destroy himself immediately upon resolution of the effect that targets it (except during the Damage Step). This can and will occur in the middle of a chain resolution. The explanation given by John is perfectly accurate for this scenario.
Ok, I'm going to assume you mean you are equipping "
Blast with Chain" to "
Gearfried the Iron Knight" during the Damage Step on this one. Here's how it would break down, based of the other threads we've had discussing "
Blast with Chain" and "
Gearfried the Iron Knight".
P1 attacks P2s "
Shining Angel" with "
Gearfried the Iron Knight".
Neither P1, nor P2 respond with any effects, so we move into Damage Step.
During Damage Calculation (Sub Step 3) P1 activates "
Blast with Chain" and equips it to "
Gearfried the Iron Knight".
P2 does not respond.
"
Blast with Chain" resolves and equips to "
Gearfried the Iron Knight" and his effect immediately kicks in and destroys "
Blast with Chain"; however, the destruction part of "
Blast with Chain" cannot resolve at this point in the Damage Step (or so we think at this time). It must wait until the Resolve Effects (Sub Step 5) portion of the Damage Step.
So "
Gearfried the Iron Knight" gets the boost, then loses the boost, but still destroys the "
Shining Angel" cause he was bigger to begin with (go figure). Now, "
Shining Angel"s effect won't kick in until the Send to Graveyard (Sub Step 6) portion of the Damage Step. So if you've been paying attention, we've got a bit of an issue here don't we..lol. Once we enter Sub Step 5, "
Shining Angel" is no longer a valid target for destruction via "
Blast with Chain"s effect because it has already been deemed destroyed by battle. If there are no other cards on the field except "
Gearfried the Iron Knight" and "
Shining Angel", guess who MUST be destroyed by the effect of "
Blast with Chain"? That's right, you guessed it..."
Gearfried the Iron Knight"! Why? Because the effect of "
Blast with Chain" is mandatory, and since "
Shining Angel"s effect won't kick in and summon another monster until Sub Step 6, we've got NO CHOICE..lol.
Did all of that make sense to everyone?
"
Tsukuyomi"s effect is a triggered effect that activates when it is flipped face-up. Therefore it MUST wait until the current chain resolves before it will be allowed to resolve. In your example, "
Nobleman of Crossout" it used on the face-down "
Tsukuyomi", the opponent chains with "
Ceasefire". Since "
Tsukuyomi" is not a Flip Effect monster, her effect WILL still activate from being flipped face-up, but will not be allowed to resolve until the current chain resolves. So, "
Ceasefire" resolves and inflicts 500 points damage, then "
Nobleman of Crossout" attempts to resolve, but since "
Tsukuyomi" is no longer face-down, it's effect '
Disappears', or resolves without effect. The chain is done resolving, NOW "
Tsukuyomi"s effect will kick in and since she is the only monster face-up on the field, she can target herself and she'll be flipped back face-down.
Hope this helps!