First shown slide doesn't trigger the cycle-before event. about cycle2

[malsup]

I think your logic would be much more efficient if you bound a single event handler to the container.

$( '.cycle-slideshow' ).on( 'click', function(e) {
    e.preventDefault();
    var opts = $( this ).data( 'cycle.opts' );
    var data = $( opts.slides[ opts.currSlide ] ).data( 'promo' );
    localStorage.setItem( 'view_promo_by_id', data );
    changePage( 'detalhe_promocao.html' );
});