In Spanish there are three variants used to indicates "the day before yesterday":
"anteayer" is the most often used variant and more popular in Spanish; on the other hand the variant "antier" is purely colloquial and should be avoided in writing and formal dialogues.
Conversamos mucho anteayer sobre el congreso.
(We talked a lot the day before yesterday about the conference.)
Antes de ayer trabajamos mucho en el proyecto.
(The day before yesterday we worked hard on the project.)
:: tip #