I don't exactly know what you mean "Eastern Crisis". There were lots of conflicts in Eastern Europe since the war in 18th century, just to mention Crimean War, war of 1878, two Balkan wars and maybe Italo-Turkish war of 1911-12. Also we should not forget Austro-Hungarian occupation of Bosnia in 1908 and something that is called "Pig War".
My opinion is that all these events had (alone) marginal effect on the outbreak of the Great War. As Francis Ferdinand was assassinated in Sarajevo, all Powers believed that the potential war with Serbia would be a local one, like the others I mentioned. The fact that it became a global war was in no way related to Austro-Serbian conflict as well as poor Archduke and his wife.
The only question between Ottoman Empire and Russia laid on the Straits and naval access of Russia to the Mediterranean. This was in fact not welcome by anybody, of course Germany and her southern ally, but by United Kingdom mostly. Russia in the east was a danger to British India and Egypt. That's why Cyprus was occupied. We can mention that during the Russo-Japanese war in 1904-05 Russian fleet was not allowed to travel through the Suez Canal. Persian agreement between UK and Russia was a compromise, the same in Afghanistan, it was strong because both parties gained what they want and secured it. However I think that UK would never agree to total destruction of the Ottoman Empire.
The Balkan question was seeking by Russia a way to Serbia and thus to the Mediterranean. Did it had impact on the World War 1? I don't think that much. The main winner of two Balkan wars (except Serbia) was Romania. This country could look for Russian assistance against Hungary and her occupation of Transylvania (and she finally joined the war on Allied side), but in fact she was independent. Romanian king was German. Serbia gained power, but it was still local power as separated from Russia.
So answering the question, the crisis(es) had their impact on the origins of the war, but in my opinion each single one was marginal, however the effect was cumulative. Balkan wars were just shuffling the cards; if you read Serbian response to Austro-Hungarian ultimatum in fact Serbia agrees to all Austrian demands, that is amazing, how humble she was. If Austria-Hungary had accepted it, Serbia would be almost politically destroyed. All the gains Serbia got during Balkan Wars would go away. All Powers (including Germany) agreed that this response should have been satisfactory; maybe Austrians feared other, 3rd Balkan war, and wanted to destroy her before? As Machiavelli said, if you fight with somebody, you should finish him, because if not dead he will seek opportunity for revenge.