Phase 1: Conceptual Grasp:
This query necessitates knowledge of the Trans-Siberian Railway's path. This extensive line traverses Russia, linking its western capital to the eastern Pacific coast.
Phase 2: Explanatory Details:
The primary alignment of the Trans-Siberian Railway progresses from west to east. Arranging the provided cities sequentially:
(A) Moscow: Situated in European Russia, serving as the railway's western terminus.
(B) Kazan: A prominent city on the Volga River, positioned east of Moscow.
(C) Omsk: A significant urban center in southwestern Siberia, located east of Kazan on the Irtysh River.
(D) Chita: Found in eastern Siberia, considerably east of Omsk, and a key railway junction.
The accurate westward-to-eastward geographical progression is Moscow $\rightarrow$ Kazan $\rightarrow$ Omsk $\rightarrow$ Chita.
Phase 3: Conclusive Response:
The correct sequence is (A), (B), (C), (D).