Which is why Moscow is calling for peace and Erdogan is rooting for war
Aside from Armenians and Azeris themselves the people who will be most worried by these developments are the residents of Kremlin.
It is the case that in the case of a wider Armenian-Azeri conflict Russia has nothing to gain and much to lose, and worse, its rival Turkey has nothing to lose and much to gain.
This is because while Russia has good relations with Armenia and Turkey good relations with Azerbaijan, Moscow also enjoys decent relations with Azerbaijan but Turkey has no Armenia relations to speak of.
Therefore if war is rekindled Turkey could back Azerbaijan without reservations and draw it closer to itself, but Russia would see its influence with at least one, or even both of the countries involed diminish.
When Azerbaijan became independent in 1991 the two states which rejoiced the most were Turkey and Iran.
Iran because it was a Shia, and Turkey because it was a Turkic country. Both looked benevolently on the new country and offered themselves up as a model for Azerbaijan to follow.
Azerbaijan chose Turkey. The most visible aspect of this choice was in replacing the Cyrillic alphabet in use until 1991 with a Turkish variant of the Latin script, instead of the Iranian-Arabic script used by the 20 million Azeris of Iran.
Despite generally orienting itself towards Ankara and Washington Azerbaijan's Aliyev dynasty, which is weary of a possible "color revolution" against it, has strove to balance these with decent working ties with Russia.
For example, unlike neighboring Georgia, Azerbaijan is not seeking to join NATO and has refused to back the Turkish position on Syria - but has instead offered to "mediate" between Ankara and Moscow.
When Armenia regained its independence in 1991 its biggest, and somewhat coincidental, backer was the US. Thanks to the efforts of the powerful Armenian-American lobby Armenia was the biggest recipient of American aid of all the post-Soviet states after Russia.
However, discounting the Armenian success in securing financial and moral support from US Congress and state legislatures, Armenia never figured in the geopolitical calculus of Washington which deemed the oil-rich Azerbaijan the far bigger prize and the more desirable partner.
Armenian lobby or not, Washington was simply not going to risk its access to the Caspian oil and its relations to NATO-member Turkey on the account of an isolated and impoverished mountain state of 3 million people.
Subsequently Yerevan, pressed between Azerbaijan and Turkey, but with nowhere to turn to eventually linked up with Russia, which in the 1990s was likewise starved for friends and would take them where it could find them. – An alliance with isolated and impoverished Armenia was not much, but for Moscow it was better than having no influence or close friends in the Southern Caucasus at all.
When Erdogan's Justice and Development party first came to power in Turkey it, as part of its "zero policy with neighbors" policy, made an attempt to normalize the Turkish-Armenian relations.
However, nothing came of this after Armenians demanded Turkey recognizes the Armenian genocide and Ankara refused.
Presently Turkey and Armenia basically do not have a relationship of any kind and the border between the two is sealed – from the Turkish side on the behalf of Azerbaijan.
In the 1990s Russian-Armenian ties were realized because at the time Moscow and Yerevan were each other's only remaining option after other, more desirable partners had paired off with each other.
However, since after 2000 Russia has managed to recreate itself as an actually functioning state now Azerbaijan (but not Georgia) also takes note of it.
A war however could rapidly change this.
In case of a war both Yerevan and Baku would be looking for backers to help them out militarily.
Since Turkey has no Armenia relationship to lose it could back Azerbaijan to the hilt.
This would bring the oil-rich country of 10 million people even closer to Turkey.
Russia, however, has such close ties to Armenia it can not possibly assist Azerbaijan in any way. Moreover, albeit its Armenia alliance does not cover Nagorno-Karabakh, if Armenians are left to fight on their own and the war goes badly for them they will naturally come to question the value of Russia ties. However, if the war goes badly for Azeris they will suspect that Russia has rendered aid to Armenians even if Moscow does no such thing.
In other words, renewed Armenian-Azeri war is a lose-lose proposition for Russia. The only way Russia can be useful to Baku and Yerevan both is if they desire peace and are looking for a way to de-escalate.
Erdogan has shown that he understands this perfectly. Reacting to the news of the clashes he has essentially said that if Azeris want to fight Turkey will back them "to the end".
Who will Baku chose to listen to? Turkey which is encouraging it to fight, or Russia which is calling for peace?