It says in Ben Ish Hai about the custom in his city of Baghdad when taking out the Sefer Torah from the Hekhal (Aron), that they would open it and show it to the congregation from the Hekhal. However, not all the members of the congregation would be able to see it from there.
They would then take the Sefer Torah to the Tebah (Bimah) which is located in the middle of the Synagogue, and would open it there to show to the entire congregation. They would show it in all four directions twice. They would then place it where it would be read from.
After they finished reading they would close the case and would not show it to the congregation again when returning it from the Tebah to the Hekhal. He mentions Kabbalistic reasons why it should be shown before the reading and not after. This is the custom of Sephardim.
The Ashkenazi custom is not to show it when taking it out, but rather, to show it after the reading is completed, as is mentioned by the Rama.
(See Ben Ish Hai, 2nd year, Parashath Toldoth, Oth 16)
