Animations - Can you cut them?

I am currently working on a 2D game project and I am running into a few small issues with animation. I am trying to use the Animator to create basic states for the character, states such as Idle, Walking, Running and Jumping. I have managed to do this however I would like to know if it is possible to implement a system what can cut an animation halfway, if you look at this project : Project you will notice how if you tap the arrow keys, the character takes an entire step to the side. I would like to know, is it possible to prevent this, from my experimentation I have found that state conditions are only checked upon starting the animation, while playing it does not check the state conditions to see whether or not it can keep playing.

I am using this script to manage the states :

 public class AnimManager : MonoBehaviour 
 {
     Animator anim;
 
     public float fakeinput;
 
     public float threshold;
 
     public bool moving;
     public bool left;
 
     public int movingHash = Animator.StringToHash("Moving");
     public int leftHash = Animator.StringToHash("Left");
 
     void Start()
     {
         anim = GetComponent<Animator>();
     }
 
     void Update()
     {
         float move = Input.GetAxis("Horizontal");
 
         anim.SetFloat("Speed", move);
 
         //move = fakeinput; // FAKE INPUT FOR EASE OF ANIMATION TESTING
 
         if (move <= 0.0f + threshold && move >= 0.0f - threshold)
         {
             moving = false;
         }
         else
         {
             moving = true;
         }
 
         anim.SetBool("Moving", moving);
 
         anim.SetBool("Left", left);
     }
 }

Is it possible for me to cancel or cut / blend back to idle if the animation is playing and the " moving " boolean is marked as false?

Any help would be massively appreciated.