Although I can not see the styles of your code well, I know why it does not work for you, the% HTML tag% handles some default margins which if you remove them will be the solution to your problem, the margin from above if I visualize solved the one below I can not distinguish it because the styles are not displayed well but visualize it with yours and you tell me.
#izenburua{
width: 100%;
text-align: center;
height: 50px;
background-color: black;
margin-top: 0px;
}
.navbar navbar-inverse{
margin-top: 0px;
margin-bottom: 0px;
}
h1{
margin-top: 0;
margin-bottom:0;
}
<link href="../bootstrap/css/bootstrap.min.css" rel="stylesheet">
<script src="https://ajax.googleapis.com/ajax/libs/jquery/3.2.1/jquery.min.js"></script>
<header id="izenburua">
<h1>ASK/ANSWER</h1>
</header>
<nav class="navbar navbar-inverse">
<div class="container-fluid">
<ul class="nav navbar-nav">
<li class="active"><a href="#">Home</a></li>
<li><a href="#">Page 1</a></li>
<li><a href="#">Page 2</a></li>
</ul>
<ul class="nav navbar-nav navbar-right">
<li><a href="#"><span class="glyphicon glyphicon-user"></span> Sign Up</a></li>
<li><a href="#"><span class="glyphicon glyphicon-log-in"></span> Login</a></li>
</ul>
</div>
</nav>
<div id="myCarousel" class="carousel slide" data-ride="carousel">
<!-- Indicators -->
<ol class="carousel-indicators">
<li data-target="#myCarousel" data-slide-to="0" class="active"></li>
<li data-target="#myCarousel" data-slide-to="1"></li>
<li data-target="#myCarousel" data-slide-to="2"></li>
</ol>
<!-- Wrapper for slides -->
<div class="carousel-inner">
<div class="item active">
<img src="http://silenttruth.co.uk/wp-content/uploads/2016/02/happy-people.jpg">
</div>
<div class="item">
<img src="https://s-i.huffpost.com/gen/3866236/images/o-HAPPY-facebook.jpg" alt="Chicago">
</div>
<div class="item">
<img src="https://s-i.huffpost.com/gen/1813932/images/o-HAPPY-facebook.jpg" alt="New York">
</div>
</div>
<!-- Left and right controls -->
<a class="left carousel-control" href="#myCarousel" data-slide="prev">
<span class="glyphicon glyphicon-chevron-left"></span>
<span class="sr-only">Previous</span>
</a>
<a class="right carousel-control" href="#myCarousel" data-slide="next">
<span class="glyphicon glyphicon-chevron-right"></span>
<span class="sr-only">Next</span>
</a>
</div>
<footer>
</footer>