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