I played a game with Sivir, and the enemy had an Anivia support. I noticed that when i used my spell sheild on Anivia's stun (her q), Sivir would respond as if she blocked the spell (she would say "back off" or "nice try", and mana would be restored), but the damage and stun still affected me.
Anivia's Q has two parts, the damage it does as it travels, and the damage and stun when she reactivates it.
You most likely spellshielded the travel damage, allowing her to reactivate it and damage and stun you.
Anivia's Q has two parts, a slow and damage that goes through in a line, and an explosion with the same damage and an AOE stun.
You blocked the slow, not the stun.
