Use mouseenterand mouseleave.
jQuery('.myRow').mouseenter(function() {
jQuery(this).find('div:first').css('visibility', 'visible');
}).mouseleave(function() {
jQuery(this).find('div:first').css('visibility', 'hidden');
});
And instead of hiding the element, set its visibility to hiddenand hover over visibleit, this will avoid flickering, because the div takes up some space when you show it. At the same time, hidden visibility will still occupy space, but will not be displayed.
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