Thx guys.

Therefore can you also vial out a fanatic, and proceed to sac him before The Abyss trigger happens? The confusion arises from the question of whether you have priority before the trigger as the active player when there is a world enchantment reading 'At the beginning of each player's upkeep'. And if this is so, then opponent gets a response the the activated abillity; all before the trigger of The Abyss?
That does not work. The abyss trigger goes on the stack at the beginning of your upkeep and you chose a target upon announcement. Vialing in a mogg fanatic at that point will not change the target initially chosen. However, if some effect were to make that target illegal (target no longer exists, target gains shroud, target gains pro-black) you do not have to destroy the targeted creature because it is no longer a legal target of The Abyss.
303.1 "As the upkeep step begins, any abilities that trigger at the beginning of that upkeep step and any abilities that triggered during the turn's untap step go on the stack. (See rule 410, "Handling Triggered Abilities.") Then the active player gets priority and players may play spells and abilities."
This means that the Abyss triggers go on the stack and the target is chosen. You can vial in Mogg fanatic in response to the trigger, but the target has already been chosen so you cannot target Mogg fanatic in this situation.