Quit get request as soon as you start another

I suggest creating a debouce function , a function that sends ajax requests not to each event but at each time interval. This way you avoid sending excessive orders.

Another alternative or complementary possibility is to have a variable that knows the last request, so that you do not receive the wrong answer if they come in a changed order.

If the list of possibilities is not too large you could pass this on to an object just when you load the page and do this functionality in JavaScript only.

debouce function, example:

function debounce(fn, delay) {
  var timer = null;
  return function () {
    var context = this, args = arguments;
    clearTimeout(timer);
    timer = setTimeout(function () {
      fn.apply(context, args);
    }, delay);
  };
}

$('input.username').keypress(debounce(function (event) {
  // do the Ajax request
}, 250));

This will only send the ajax request after 1/4 second of inactivity.

variable / flag with last request:

Using your code, put together a variable with the previous scope:

var ajaxID = 0;
$.ajax({
    url: "<?=$this->Html->url(array('controller' => 'busca', 'action' => 'searchanise'));?>",
    type: 'POST',
    async: false,
    data: {texto: text},
    beforeSend: function(){
        ajaxID++;
        this.ajaxID = ajaxID;
    },
    success: function(data){
        if (this.ajaxID != ajaxID) return; // descartar pois não é a ultima
        retorno = JSON.parse(data);
        $("#searchanise").html(retorno);
    }

});

You can save the call get to a variable:

var request = $.ajax({
    type: 'POST',
    url: 'someurl',
    success: function(result){}
});

So every time you make a request, just check the request variable. If it is not null or indefinite, just give abort before starting the new request:

request.abort();