Another imperfection to this otherwise interesting tool: it is hard if not impossible to click on small countries or islands. Good luck if you want to know who goes to Guadeloupe. Pascali Islands are hidden by the legend if I'm not mistaking. This is inherent to any "click a country on the world map" tool. A complex and not perfect way to fix it would be to allow zooming, but here I would add a drop-down with a list of countries.

There is a drop-down with a list of countries and the legend is draggable if you wish.

BTW, you can also click on the name of countries in the legend.

Great, I overlooked that.

I have tried to add arrows at some point, but it cluttered the visualization too much (especially for countries where migrations are quite local : limited to border-sharing countries).

That said, there may be a solution I did not think about.

You could over impose three dotted lines with a different color/dot-spacing to each connecting line, then set a timeout and alternate their visibility accordingly, so you can get a "dots flowing inside the line" effect. Not sure if this can work with canvas though.

How about drawing the arrowhead on the middle of the line? (And not drawing it on short lines. The arrowheads on the long lines will reveal whether 'departures' or 'arrivals' are depicted)

This. And if possible, add a subtle gradient on each curve. So, even without arrows on short lines the direction is clear. Plus it looks cool.

How about different colors of lines for from/to?

How about narrowing lines?