These are the mentions of time in Ezra. The italics verses are important but not in the time flow of the Book. They mark actions and give historical references.  

Ezra 1:1  1y of Cyrus of Persia (reference Daniel)

Ezra 3:1  7m (1y) Jeshua and Zerubbabel rebuilt the altar

Ezra 3:4  Feast of Tabernacles was celebrated with offerings (15d) 

Ezra 3:6  refers back to 3:1, burnt offerings were started (daily)

Ezra 3:8  2y, 2m after their arrival started the Temple. 5m after 3:1

Ezra 4:2  Samaritans reference Esarhaddon king of Assyria, no time is given

Ezra 4:7  Xerxes or Ahasuerus is referenced in verse six and a formal letter is sent in the days of Artaxerxes that stopped work on the Temple

Ezra 4:24  2y of Darius king of Persia work was stopped, this is Darius the Second (there are three mentioned starting in Daniel)

Ezra 5:3  5:1 references Haggai and Zechariah, 5:3 mentions Tattenai the governor, who is confirmed by archeology.

Ezra 5:11  reference to Solomon

Ezra 5:13  reference to Cyrus

Ezra 5:16  reference to Sheshbazzar

Ezra 6:3  a letter Darius found, from Cyrus (see 3:1)

Ezra 6:15  6y 12m 3d of Darius, the Temple was completed

Ezra 6:19 1m 14d after the Temple is finished, they celebrate Passover

Ezra 6:22  the seven days of the Feast cycle

Ezra 7:7   

Ezra 7:8

Ezra 7:9  Ezra started 7y1m1d and arrived at 7y5m1d of Artaxerxes with additional temple workers. This is the time of Passover and Pentecost.

Ezra 8:15  Assembled at the Ahava Canal, camped for three days, fasted, and waited for Levities.

Ezra 8:31  1m 12 d they started left for Jerusalem. (See 7:8+9)

Ezra 8:32  Three-day rest in Jerusalem after arriving.

Ezra 8:33  Fourth day they check the treasures that were brought with them.

Ezra 10:8  A three-day notice to appear. The exact time is not mentioned.

Ezra 10:9 9m 20d Ezra had an assembly, it rained, about mixed marriages.

Ezra 10:16 10m 1d The investigations started

Ezra 10:17 1m 1d The investigation was finished.