If you have all 3 Sarcophagi on your side of the field, the effect happens automatically; you have no choice in the matter.
If you have multiple copies of "The First Sarcophagus", each will have its own "Second Sarcophagus" and "Third Sarcophagus". So if you have 2 of "TheFirst Sarcophagus", you will have 2 of "The Second Sarcophagus" on the field. If you Special Summon "Spirit of the Pharaoh" or if 1 of the Sarcophagi is removed from the field, all Sarcophagi cards are sent to the Graveyard.
If 1 of the Sarcophagi is sent to the Graveyard, all are sent simultaneously, not as a chain.