Animation CSS3: display + opacity

Based on Michaels answer this is the actual CSS code to use

.parent:hover .child
{
    display: block;

    -webkit-animation: fadeInFromNone 0.5s ease-out;
    -moz-animation: fadeInFromNone 0.5s ease-out;
    -o-animation: fadeInFromNone 0.5s ease-out;
    animation: fadeInFromNone 0.5s ease-out;
}

@-webkit-keyframes fadeInFromNone {
    0% {
        display: none;
        opacity: 0;
    }

    1% {
        display: block;
        opacity: 0;
    }

    100% {
        display: block;
        opacity: 1;
    }
}

@-moz-keyframes fadeInFromNone {
    0% {
        display: none;
        opacity: 0;
    }

    1% {
        display: block;
        opacity: 0;
    }

    100% {
        display: block;
        opacity: 1;
    }
}

@-o-keyframes fadeInFromNone {
    0% {
        display: none;
        opacity: 0;
    }

    1% {
        display: block;
        opacity: 0;
    }

    100% {
        display: block;
        opacity: 1;
    }
}

@keyframes fadeInFromNone {
    0% {
        display: none;
        opacity: 0;
    }

    1% {
        display: block;
        opacity: 0;
    }

    100% {
        display: block;
        opacity: 1;
    }
}

If possible - use visibility instead of display

For instance:

.child {
    visibility: hidden;
    opacity: 0;
    transition: opacity 0.3s, visibility 0.3s;
}

.parent:hover .child {
    visibility: visible;
    opacity: 1;
    transition: opacity 0.3s, visibility 0.3s;
}

You can do with CSS animations:

0% display:none ; opacity: 0;
1% display: block ; opacity: 0;
100% display: block ; opacity: 1;