我建议将common类添加到所有需要动画的元素（.anim1，.anim2...，.anim7）中。* 我添加了公共类.anim。* 在.anim类样式上添加动画，并在.anim1, .anim2, ...., .anim7类样式上添加延迟，延迟随总动画持续时间增加。
换句话说，在所有元素上运行相同的动画，但有一些延迟。
如果你想添加/删除动画元素，你只需要在animation-duration属性上做简单的数学运算。它将是animation-delay time * total elements。
请参阅下面的Sniffs：

html,
body {
  font-family: 'Droid Serif', serif;
}

h1 {
  font-size: 60px;
  text-align: center;
}

.content-slider {
  width: 100%;
  height: 360px;
}

.slider {
  height: 320px;
  width: 680px;
  margin: 40px auto 0;
  overflow: visible;
  position: relative;
}

.mask {
  overflow: hidden;
  height: 320px;
}

.slider ul {
  margin: 0;
  padding: 0;
  position: relative;
}

.slider li {
  width: 680px;
  height: 320px;
  position: absolute;
  top: -325px;
  list-style: none;
}

.slider .quote {
  font-size: 40px;
  font-style: italic;
}

.slider .source {
  font-size: 20px;
  text-align: right;
}

.slider li.anim {
  animation-name: cycle;
  animation-duration: 21s; /*You need to do Math here. (delay time * total elements)*/
  animation-iteration-count: infinite;
  animation-fill-mode: forwards;
  animation-timing-function: linear;
}

.anim1{
  animation-delay:0s; 
}

.anim2{
  animation-delay:3s; 
}
.anim3{
  animation-delay:6s; 
} 
.anim4{
  animation-delay:9s; 
}
.anim5{
  animation-delay:12s; 
} 
.anim6{
  animation-delay:15s; 
}
.anim7{
  animation-delay:18s; 
}

.slider:hover li {
  animation-play-state: paused;
}

@keyframes cycle {
  0% {
    top: -325px;
  }
  4% {
    top: 0px;
  }
  16% {
    top: 0px;
    opacity: 1;
    z-index: 0;
  }
  18% {
    top: 325px;
    opacity: 0;
    z-index: 0;
  }
  92% {
    top: -325px;
    opacity: 0;
    z-index: 0;
  }
  100% {
    top: -325px;
    opacity: 0;
  }
}

<h1>Pure CSS3 Text Carousel</h1>

<div class="content-slider">
  <div class="slider">
    <div class="mask">
      <ul>
        <li class="anim anim1">
          <div class="quote">1. Hello, this is a quote from a person.</div>
          <div class="source">1 - Person</div>
        </li>
        <li class="anim anim2">
          <div class="quote">2. Hello, this is a quote from another person.</div>
          <div class="source">2 - Another person</div>
        </li>
        <li class="anim anim3">
          <div class="quote">3. Hello, this is a quote from an animal.</div>
          <div class="source">3 - Animal</div>
        </li>
        <li class="anim anim4">
          <div class="quote">4. Hello, this is a quote from a plant.</div>
          <div class="source">4 - Plant</div>
        </li>
        <li class="anim anim5">
          <div class="quote">5. How do ya like that.</div>
          <div class="source">5 - Cassidy</div>
        </li>
        <li class="anim anim6">
          <div class="quote">6. How do ya like that.</div>
          <div class="source">6 - Cassidy</div>
        </li>
        <li class="anim anim7">
          <div class="quote">7. How do ya like that.</div>
          <div class="source">7 - Cassidy</div>
        </li>
      </ul>
    </div>
  </div>
</div>