BRUSSELS - Often these days, the first order of business at European Union summits isn't the continent's dreadful financial crisis.

It's getting to know the people around the table.

The group of leaders that will meet this week in Brussels is a much different crew from the one that met in October 2009, when the crisis in Europe first erupted with the news that Greece was in deep trouble.

Gone is the colorful and sometimes embarrassing Italian premier Silvio Berlusconi, replaced by the technocratic Mario Monti. Europe has said "au revoir" to hyperkinetic French President Nicolas Sarkozy and "bonjour" to the altogether more sedate Francois Hollande. The glower of Britain's Gordon Brown has given way the youthful countenance of David Cameron.

At this summit, leaders had been preparing to shake hands with new Greek Prime Minister Antonis Samaras - until emergency eye surgery forced him to send regrets.

The revolving door of European leaders raises the question of how Europe can implement bold and swift decisions when it's not even clear who'll be in charge a few months from now.

Carefully cultivated alliances can get swept away in the swirl of parliamentary politics. How, the pundits ask, can Europe come together on a united vision for the future when instability lies at the very heart of the continent's democratic system?

Of the 27 countries in the EU, 14 have switched leaders since the crisis began a little over two and a half years ago. Only one major national leader has remained a constant throughout the crisis: German Chancellor Angela Merkel. And her staying power, at the top of Europe's biggest economy, has bolstered Germany's dominant role in European decision-making.

After all, it's safe to say that few people are waiting for Bulgarian Prime Minister Boyko Borissov to lead the way.

Changes at the top can have a profound influence on Europe's balance of power. Hollande, a strong champion of boosting growth, has helped tilt Europe away from the stark austerity path charted by Merkel and Sarkozy. Mario Draghi, who replaced Jean-Claude Trichet as chief of the European Central Bank late last year, has largely ditched his predecessor's cautious strategies and breathed new life into markets.

It seems that almost every time the leaders meet, which is often, there's a new face. At the most recent summit, in May, it was Hollande. Late last year, leaders had to acquaint themselves with Italy's Monti, Spain's Mariano Rajoy and Greece's Lucas Papademos, all in the space of a couple of months.

Beyond fanciful notions of presidents and prime ministers needing name tags or surreptitiously peeking at the cheat sheets (with photos) that the EU helpfully prints out for journalists, the rapidly changing cast of characters has caused many to ask: Has it slowed the response to the financial crisis?

Perhaps. Summit diplomacy is to a large extent about building personal relationships.

The bottom line is that it takes time for the leaders to size each other up and to earn each other's trust.

Merkel and Sarkozy, for example, had difficulties working together in the early months of the financial crisis. Sarkozy criticized Germany in public for its failure to act. And when Sarkozy led camera crews into a meeting, Merkel reportedly told him, "I won't let you do this to me," and made them leave.

But with the passage of time, and under the pressure of the crisis, they developed such a close partnership that they came to be dubbed "Merkozy."

As leaders of the European currency union's biggest economies, the two regularly met before each EU summit to hash out common positions. They then presented their decisions to other leaders pretty much as a fait accompli. And during the French presidential campaign this year, Merkel declared her support for Sarkozy - refusing to meet with Hollande.

Now that relationship's gone. Merkel and Hollande sharply disagree about the way forward for Europe. The divergence at the center of Europe has created fresh worries about the continent's fate.

Observers say it can take time to rebuild carefully nurtured national alliances.

"Through their personal exchanges at summit meetings, leaders familiarize each other with the domestic political pressures and constraints they face back home," said David Shorr, an expert on summitry at the Stanley Foundation, an Iowa-based organization that promotes multilateralism. "The personal trust piece of this has to be established freshly with each new leader who joins the club."

But Shorr noted that personal chemistry may count for little when nations start pulling apart on the issues.

"You don't need to know President Hollande well to recognize the French elections themselves as a pretty clear weather vane for the shifting political winds," he said.