What species is that "eurobird"?

A few years ago,shortly after moving to Florida from my European assignment and effectively retiring from my long-term employee within a few days,I was accosted on the tennis court by already retired residents. After a few pleasantries and introductions , one of them said to me after hearing that we'll be here only in the winters: "So, we have another snow-bird here!"
Having lived in Canada, too, for some 21 years I knew immediately the kind of bird I was taken to be. And it almost fitted the description. I was, in fact, a Canadian, I was going to live in Florida during the winter only, I talked "funny" (at least as compared to real Floridians). However, it wasn't a perfect fit.
Not wanting to sound snobbish, but feeling the weight of responsibility to explain myself, without a moment of hesitation I have found the best possible answer to the friendly gentleman calling me a snow-bird.
"Actually, I am a euro-bird" and being quite surprised myself at this instant creativity, I looked around with a confident smile that bordered on unintended impertinence.
The expression just created a species hitherto unknown to me, or, apparently anyone else in the group. There was a moment of silence and to my utter relief another gentleman came to my rescue asking whether we go to Europe in the summer instead of "up North".
The rest is history.
Yes, we actually have a home on each continent and about the same time when the snow-birds return to their summer nests, the euro birds head East to Europe.
Without confusing my dear readers,I have to add that my genes have quite a bit of snow-bird-y characteristics as well,since come the North American spring I feel a calling from "up North" and I often heed that irresistible call and "fly up" to one or another Canadian community. (To visit can-birds, naturally.)