HeaderMenu.vue

<script>
  export default {
    name: 'app-header-menu',
    data () {
      return {
        isChangingRoute: true
      }
    },
    computed: {
      isHomeRoute: function () {
        return this.$route.name === 'home'
      }
    },
    watch: {
      '$route': function () {
        this.isChangingRoute = true
        setTimeout(() => {
          this.isChangingRoute = false
        })
      }
    },
    mounted () {
      this.isChangingRoute = false
    }
  }
</script>

<template>
    <v-btn v-if="!isChangingRoute" icon key="headerMenu">
        <i class="fas fa-bars" key="toolbarBars" v-if="isHomeRoute"></i>
        <i class="fas fa-arrow-left" key="toolbarArrow" v-else></i>
    </v-btn>
</template>