The model of transition in Russia, Central Asia, and East Europe that was influenced by the World Bank and the IMF came to be known as:

The correct option is Shock Therapy.

Explanation:

With the collapse of the Soviet Union and communism in the late 1980s and early 1990s, many post-communist authoritarian regimes in Russia, Central Asia, and East Europe underwent a painful transition process.
This transition aimed to transform their closed, state-controlled economies into open, market-oriented capitalist economies.

This rapid and painful model of transition was heavily influenced and advised by international financial institutions, specifically the World Bank and the International Monetary Fund (IMF).
This economic process and policy package came to be known as "Shock Therapy".

The shock therapy model involved several radical components:
1. A total shift to a capitalist economy, ending state ownership of assets and promoting private ownership through privatization.
2. Introducing complete free trade and foreign direct investment (FDI).
3. Deregulation, currency convertibility, and the elimination of state subsidies on essential goods.

Let's look at why the other options are incorrect:
• Current Therapy and Fiscal Therapy: These are not recognized historical or economic terms for this transition process.
• Glasnost: This translates to "openness" and was a political reform policy introduced by Mikhail Gorbachev in the Soviet Union during the 1980s to allow more freedom of speech and government transparency, rather than the economic transition model overseen by the IMF and World Bank.