Formations of military alliances increased tension during the period of cold war because:
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It lead to the race for deadly weapons among the nations.
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United States of America feared spread of communism and formed blocs like NATO (North Atlantic Treaty Organisation) for defence against Soviet Union. South East Asia Treaty Organisation (SEATO) was also set up. Similarly Baghdad Pact was brought into being in 1955 (later changed to CENTO). As against these alliances, the Soviet Union and the socialist countries of Europe formed the Warsaw Pact. These alliances and the pacts were looked upon as danger to peace and security.
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Countries having alliances with each bloc suspected the integrity of their rivals and hence there remained a constant threat of war.
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The formation of these military alliances caused tensions because they were threat to the independence of many countries.